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problem stringlengths 35 13.2k	solutions listlengths 1 3.42k	tests stringlengths 120 74M	starter_code stringclasses 0 values	metadata stringclasses 1 value	question stringlengths 600 13.8k	ground_truth stringlengths 450 74M	data_source stringclasses 1 value	uid stringlengths 11 15	index int64 0 17.1k
Solve the following coding problem using the programming language python: There are some websites that are accessible through several different addresses. For example, for a long time Codeforces was accessible with two hostnames codeforces.com and codeforces.ru. You are given a list of page addresses being queried. For simplicity we consider all addresses to have the form http://<hostname>[/<path>], where: <hostname> — server name (consists of words and maybe some dots separating them), /<path> — optional part, where <path> consists of words separated by slashes. We consider two <hostname> to correspond to one website if for each query to the first <hostname> there will be exactly the same query to the second one and vice versa — for each query to the second <hostname> there will be the same query to the first one. Take a look at the samples for further clarifications. Your goal is to determine the groups of server names that correspond to one website. Ignore groups consisting of the only server name. Please note, that according to the above definition queries http://<hostname> and http://<hostname>/ are different. -----Input----- The first line of the input contains a single integer n (1 ≤ n ≤ 100 000) — the number of page queries. Then follow n lines each containing exactly one address. Each address is of the form http://<hostname>[/<path>], where: <hostname> consists of lowercase English letters and dots, there are no two consecutive dots, <hostname> doesn't start or finish with a dot. The length of <hostname> is positive and doesn't exceed 20. <path> consists of lowercase English letters, dots and slashes. There are no two consecutive slashes, <path> doesn't start with a slash and its length doesn't exceed 20. Addresses are not guaranteed to be distinct. -----Output----- First print k — the number of groups of server names that correspond to one website. You should count only groups of size greater than one. Next k lines should contain the description of groups, one group per line. For each group print all server names separated by a single space. You are allowed to print both groups and names inside any group in arbitrary order. -----Examples----- Input 10 http://abacaba.ru/test http://abacaba.ru/ http://abacaba.com http://abacaba.com/test http://abacaba.de/ http://abacaba.ru/test http://abacaba.de/test http://abacaba.com/ http://abacaba.com/t http://abacaba.com/test Output 1 http://abacaba.de http://abacaba.ru Input 14 http://c http://ccc.bbbb/aba..b http://cba.com http://a.c/aba..b/a http://abc/ http://a.c/ http://ccc.bbbb http://ab.ac.bc.aa/ http://a.a.a/ http://ccc.bbbb/ http://cba.com/ http://cba.com/aba..b http://a.a.a/aba..b/a http://abc/aba..b/a Output 2 http://cba.com http://ccc.bbbb http://a.a.a http://a.c http://abc The input will be stdin and you should print your solution to stdout Now solve the problem and return the code.	[ "```python\n# Bartek Kostka\n# You are not prepared!\n\n#include \"bits/stdc++.h\"\n\nn = int(input())\nW = {}\nfor i in range(n):\n adr = input()\n adr = adr.split(\"/\")\n if adr[-1] == '':\n adr[-1] = '?'\n domena = \"/\".join(adr[:3])\n adres = \"/\".join(adr[3:])\n #print(domena, adres)\n if domena not in W:\n W[domena] = set()\n W[domena].add(adres)\n\nE = {}\nfor key, ele in list(W.items()):\n #print(key, ele)\n lele = \"#\".join(sorted(list(ele)))\n if lele not in E:\n E[lele] = []\n E[lele].append(key)\n\nres = 0\nfor key, ele in list(E.items()):\n if len(ele) > 1:\n res += 1\n\nprint(res)\nfor key, ele in list(E.items()):\n if len(ele) > 1:\n print(\" \".join(ele))\n\n```" ]	[{"type": "stdin_stdout", "input": "10\nhttp://abacaba.ru/test\nhttp://abacaba.ru/\nhttp://abacaba.com\nhttp://abacaba.com/test\nhttp://abacaba.de/\nhttp://abacaba.ru/test\nhttp://abacaba.de/test\nhttp://abacaba.com/\nhttp://abacaba.com/t\nhttp://abacaba.com/test\n", "output": "1\nhttp://abacaba.de http://abacaba.ru \n"}, {"type": "stdin_stdout", "input": "14\nhttp://c\nhttp://ccc.bbbb/aba..b\nhttp://cba.com\nhttp://a.c/aba..b/a\nhttp://abc/\nhttp://a.c/\nhttp://ccc.bbbb\nhttp://ab.ac.bc.aa/\nhttp://a.a.a/\nhttp://ccc.bbbb/\nhttp://cba.com/\nhttp://cba.com/aba..b\nhttp://a.a.a/aba..b/a\nhttp://abc/aba..b/a\n", "output": "2\nhttp://cba.com http://ccc.bbbb \nhttp://a.a.a http://a.c http://abc \n"}, {"type": "stdin_stdout", "input": "10\nhttp://tqr.ekdb.nh/w\nhttp://p.ulz/ifw\nhttp://w.gw.dw.xn/kpe\nhttp://byt.mqii.zkv/j/xt\nhttp://ovquj.rbgrlw/k..\nhttp://bv.plu.e.dslg/j/xt\nhttp://udgci.ufgi.gwbd.s/\nhttp://l.oh.ne.o.r/.vo\nhttp://l.oh.ne.o.r/w\nhttp://tqr.ekdb.nh/.vo\n", "output": "2\nhttp://l.oh.ne.o.r http://tqr.ekdb.nh \nhttp://bv.plu.e.dslg http://byt.mqii.zkv \n"}, {"type": "stdin_stdout", "input": "12\nhttp://ickght.ck/mr\nhttp://a.exhel/.b\nhttp://a.exhel/\nhttp://ti.cdm/\nhttp://ti.cdm/x/wd/lm.h.\nhttp://ickght.ck/a\nhttp://ickght.ck\nhttp://c.gcnk.d/.b\nhttp://c.gcnk.d/x/wd/lm.h.\nhttp://ti.cdm/.b\nhttp://a.exhel/x/wd/lm.h.\nhttp://c.gcnk.d/\n", "output": "1\nhttp://a.exhel http://c.gcnk.d http://ti.cdm \n"}, {"type": "stdin_stdout", "input": "14\nhttp://jr/kgb\nhttp://ps.p.t.jeua.x.a.q.t\nhttp://gsqqs.n/t/\nhttp://w.afwsnuc.ff.km/cohox/u.\nhttp://u.s.wbumkuqm/\nhttp://u.s.wbumkuqm/cohox/u.\nhttp://nq.dzjkjcwv.f.s/bvm/\nhttp://zoy.shgg\nhttp://gsqqs.n\nhttp://u.s.wbumkuqm/b.pd.\nhttp://w.afwsnuc.ff.km/\nhttp://w.afwsnuc.ff.km/b.pd.\nhttp://nq.dzjkjcwv.f.s/n\nhttp://nq.dzjkjcwv.f.s/ldbw\n", "output": "2\nhttp://ps.p.t.jeua.x.a.q.t http://zoy.shgg \nhttp://u.s.wbumkuqm http://w.afwsnuc.ff.km \n"}, {"type": "stdin_stdout", "input": "15\nhttp://l.edzplwqsij.rw/\nhttp://m.e.mehd.acsoinzm/s\nhttp://yg.ttahn.xin.obgez/ap/\nhttp://qqbb.pqkaqcncodxmaae\nhttp://lzi.a.flkp.lnn.k/o/qfr.cp\nhttp://lzi.a.flkp.lnn.k/f\nhttp://p.ngu.gkoq/.szinwwi\nhttp://qqbb.pqkaqcncodxmaae/od\nhttp://qqbb.pqkaqcncodxmaae\nhttp://wsxvmi.qpe.fihtgdvi/e./\nhttp://p.ngu.gkoq/zfoh\nhttp://m.e.mehd.acsoinzm/xp\nhttp://c.gy.p.h.tkrxt.jnsjt/j\nhttp://wsxvmi.qpe.fihtgdvi/grkag.z\nhttp://p.ngu.gkoq/t\n", "output": "0\n"}, {"type": "stdin_stdout", "input": "15\nhttp://w.hhjvdn.mmu/.ca.p\nhttp://m.p.p.lar/\nhttp://lgmjun.r.kogpr.ijn/./t\nhttp://bapchpl.mcw.a.lob/d/ym/./g.q\nhttp://uxnjfnjp.kxr.ss.e.uu/jwo./hjl/\nhttp://fd.ezw.ykbb.xhl.t/\nhttp://i.xcb.kr/.ca.p\nhttp://jofec.ry.fht.gt\nhttp://qeo.gghwe.lcr/d/ym/./g.q\nhttp://gt\nhttp://gjvifpf.d/d/ym/./g.q\nhttp://oba\nhttp://rjs.qwd/v/hi\nhttp://fgkj/\nhttp://ivun.naumc.l/.ca.p\n", "output": "4\nhttp://gt http://jofec.ry.fht.gt http://oba \nhttp://fd.ezw.ykbb.xhl.t http://fgkj http://m.p.p.lar \nhttp://i.xcb.kr http://ivun.naumc.l http://w.hhjvdn.mmu \nhttp://bapchpl.mcw.a.lob http://gjvifpf.d http://qeo.gghwe.lcr \n"}, {"type": "stdin_stdout", "input": "20\nhttp://gjwr/xsoiagp/\nhttp://gdnmu/j\nhttp://yfygudx.e.aqa.ezh/j\nhttp://mpjxue.cuvipq/\nhttp://a/\nhttp://kr/..n/c.\nhttp://a/xsoiagp/\nhttp://kr/z\nhttp://kr/v.cv/rk/k\nhttp://lvhpz\nhttp://qv.v.jqzhq\nhttp://y.no/\nhttp://kr/n\nhttp://y.no/xsoiagp/\nhttp://kr/ebe/z/\nhttp://olsvbxxw.win.n/j\nhttp://p.ct/j\nhttp://mpjxue.cuvipq/xsoiagp/\nhttp://kr/j\nhttp://gjwr/\n", "output": "3\nhttp://lvhpz http://qv.v.jqzhq \nhttp://a http://gjwr http://mpjxue.cuvipq http://y.no \nhttp://gdnmu http://olsvbxxw.win.n http://p.ct http://yfygudx.e.aqa.ezh \n"}, {"type": "stdin_stdout", "input": "1\nhttp://a\n", "output": "0\n"}, {"type": "stdin_stdout", "input": "1\nhttp://a.a.a.f.r.f.q.e.w.a/fwe..sdfv....\n", "output": "0\n"}, {"type": "stdin_stdout", "input": "3\nhttp://abacaba.com/test\nhttp://abacaba.de/test\nhttp://abacaba.de/test\n", "output": "1\nhttp://abacaba.com http://abacaba.de \n"}]	null	null	You are an expert Python programmer. You will be given a question (problem specification) and will generate a correct Python program that matches the specification and passes all tests. Solve the following coding problem using the programming language python: There are some websites that are accessible through several different addresses. For example, for a long time Codeforces was accessible with two hostnames codeforces.com and codeforces.ru. You are given a list of page addresses being queried. For simplicity we consider all addresses to have the form http://<hostname>[/<path>], where: <hostname> — server name (consists of words and maybe some dots separating them), /<path> — optional part, where <path> consists of words separated by slashes. We consider two <hostname> to correspond to one website if for each query to the first <hostname> there will be exactly the same query to the second one and vice versa — for each query to the second <hostname> there will be the same query to the first one. Take a look at the samples for further clarifications. Your goal is to determine the groups of server names that correspond to one website. Ignore groups consisting of the only server name. Please note, that according to the above definition queries http://<hostname> and http://<hostname>/ are different. -----Input----- The first line of the input contains a single integer n (1 ≤ n ≤ 100 000) — the number of page queries. Then follow n lines each containing exactly one address. Each address is of the form http://<hostname>[/<path>], where: <hostname> consists of lowercase English letters and dots, there are no two consecutive dots, <hostname> doesn't start or finish with a dot. The length of <hostname> is positive and doesn't exceed 20. <path> consists of lowercase English letters, dots and slashes. There are no two consecutive slashes, <path> doesn't start with a slash and its length doesn't exceed 20. Addresses are not guaranteed to be distinct. -----Output----- First print k — the number of groups of server names that correspond to one website. You should count only groups of size greater than one. Next k lines should contain the description of groups, one group per line. For each group print all server names separated by a single space. You are allowed to print both groups and names inside any group in arbitrary order. -----Examples----- Input 10 http://abacaba.ru/test http://abacaba.ru/ http://abacaba.com http://abacaba.com/test http://abacaba.de/ http://abacaba.ru/test http://abacaba.de/test http://abacaba.com/ http://abacaba.com/t http://abacaba.com/test Output 1 http://abacaba.de http://abacaba.ru Input 14 http://c http://ccc.bbbb/aba..b http://cba.com http://a.c/aba..b/a http://abc/ http://a.c/ http://ccc.bbbb http://ab.ac.bc.aa/ http://a.a.a/ http://ccc.bbbb/ http://cba.com/ http://cba.com/aba..b http://a.a.a/aba..b/a http://abc/aba..b/a Output 2 http://cba.com http://ccc.bbbb http://a.a.a http://a.c http://abc The input will be stdin and you should print your solution to stdout Now solve the problem and return the code.### Format: Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within delimiters as follows. Ensure that when the python program runs, it reads the inputs, runs the algorithm and writes output to STDOUT. ```python # YOUR CODE HERE ``` ### Answer: (use the provided format with backticks)	[{"type": "stdin_stdout", "input": "10\nhttp://abacaba.ru/test\nhttp://abacaba.ru/\nhttp://abacaba.com\nhttp://abacaba.com/test\nhttp://abacaba.de/\nhttp://abacaba.ru/test\nhttp://abacaba.de/test\nhttp://abacaba.com/\nhttp://abacaba.com/t\nhttp://abacaba.com/test\n", "output": "1\nhttp://abacaba.de http://abacaba.ru \n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "14\nhttp://c\nhttp://ccc.bbbb/aba..b\nhttp://cba.com\nhttp://a.c/aba..b/a\nhttp://abc/\nhttp://a.c/\nhttp://ccc.bbbb\nhttp://ab.ac.bc.aa/\nhttp://a.a.a/\nhttp://ccc.bbbb/\nhttp://cba.com/\nhttp://cba.com/aba..b\nhttp://a.a.a/aba..b/a\nhttp://abc/aba..b/a\n", "output": "2\nhttp://cba.com http://ccc.bbbb \nhttp://a.a.a http://a.c http://abc \n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "10\nhttp://tqr.ekdb.nh/w\nhttp://p.ulz/ifw\nhttp://w.gw.dw.xn/kpe\nhttp://byt.mqii.zkv/j/xt\nhttp://ovquj.rbgrlw/k..\nhttp://bv.plu.e.dslg/j/xt\nhttp://udgci.ufgi.gwbd.s/\nhttp://l.oh.ne.o.r/.vo\nhttp://l.oh.ne.o.r/w\nhttp://tqr.ekdb.nh/.vo\n", "output": "2\nhttp://l.oh.ne.o.r http://tqr.ekdb.nh \nhttp://bv.plu.e.dslg http://byt.mqii.zkv \n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "12\nhttp://ickght.ck/mr\nhttp://a.exhel/.b\nhttp://a.exhel/\nhttp://ti.cdm/\nhttp://ti.cdm/x/wd/lm.h.\nhttp://ickght.ck/a\nhttp://ickght.ck\nhttp://c.gcnk.d/.b\nhttp://c.gcnk.d/x/wd/lm.h.\nhttp://ti.cdm/.b\nhttp://a.exhel/x/wd/lm.h.\nhttp://c.gcnk.d/\n", "output": "1\nhttp://a.exhel http://c.gcnk.d http://ti.cdm \n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "14\nhttp://jr/kgb\nhttp://ps.p.t.jeua.x.a.q.t\nhttp://gsqqs.n/t/\nhttp://w.afwsnuc.ff.km/cohox/u.\nhttp://u.s.wbumkuqm/\nhttp://u.s.wbumkuqm/cohox/u.\nhttp://nq.dzjkjcwv.f.s/bvm/\nhttp://zoy.shgg\nhttp://gsqqs.n\nhttp://u.s.wbumkuqm/b.pd.\nhttp://w.afwsnuc.ff.km/\nhttp://w.afwsnuc.ff.km/b.pd.\nhttp://nq.dzjkjcwv.f.s/n\nhttp://nq.dzjkjcwv.f.s/ldbw\n", "output": "2\nhttp://ps.p.t.jeua.x.a.q.t http://zoy.shgg \nhttp://u.s.wbumkuqm http://w.afwsnuc.ff.km \n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "15\nhttp://l.edzplwqsij.rw/\nhttp://m.e.mehd.acsoinzm/s\nhttp://yg.ttahn.xin.obgez/ap/\nhttp://qqbb.pqkaqcncodxmaae\nhttp://lzi.a.flkp.lnn.k/o/qfr.cp\nhttp://lzi.a.flkp.lnn.k/f\nhttp://p.ngu.gkoq/.szinwwi\nhttp://qqbb.pqkaqcncodxmaae/od\nhttp://qqbb.pqkaqcncodxmaae\nhttp://wsxvmi.qpe.fihtgdvi/e./\nhttp://p.ngu.gkoq/zfoh\nhttp://m.e.mehd.acsoinzm/xp\nhttp://c.gy.p.h.tkrxt.jnsjt/j\nhttp://wsxvmi.qpe.fihtgdvi/grkag.z\nhttp://p.ngu.gkoq/t\n", "output": "0\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "15\nhttp://w.hhjvdn.mmu/.ca.p\nhttp://m.p.p.lar/\nhttp://lgmjun.r.kogpr.ijn/./t\nhttp://bapchpl.mcw.a.lob/d/ym/./g.q\nhttp://uxnjfnjp.kxr.ss.e.uu/jwo./hjl/\nhttp://fd.ezw.ykbb.xhl.t/\nhttp://i.xcb.kr/.ca.p\nhttp://jofec.ry.fht.gt\nhttp://qeo.gghwe.lcr/d/ym/./g.q\nhttp://gt\nhttp://gjvifpf.d/d/ym/./g.q\nhttp://oba\nhttp://rjs.qwd/v/hi\nhttp://fgkj/\nhttp://ivun.naumc.l/.ca.p\n", "output": "4\nhttp://gt http://jofec.ry.fht.gt http://oba \nhttp://fd.ezw.ykbb.xhl.t http://fgkj http://m.p.p.lar \nhttp://i.xcb.kr http://ivun.naumc.l http://w.hhjvdn.mmu \nhttp://bapchpl.mcw.a.lob http://gjvifpf.d http://qeo.gghwe.lcr \n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "20\nhttp://gjwr/xsoiagp/\nhttp://gdnmu/j\nhttp://yfygudx.e.aqa.ezh/j\nhttp://mpjxue.cuvipq/\nhttp://a/\nhttp://kr/..n/c.\nhttp://a/xsoiagp/\nhttp://kr/z\nhttp://kr/v.cv/rk/k\nhttp://lvhpz\nhttp://qv.v.jqzhq\nhttp://y.no/\nhttp://kr/n\nhttp://y.no/xsoiagp/\nhttp://kr/ebe/z/\nhttp://olsvbxxw.win.n/j\nhttp://p.ct/j\nhttp://mpjxue.cuvipq/xsoiagp/\nhttp://kr/j\nhttp://gjwr/\n", "output": "3\nhttp://lvhpz http://qv.v.jqzhq \nhttp://a http://gjwr http://mpjxue.cuvipq http://y.no \nhttp://gdnmu http://olsvbxxw.win.n http://p.ct http://yfygudx.e.aqa.ezh \n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "1\nhttp://a\n", "output": "0\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "1\nhttp://a.a.a.f.r.f.q.e.w.a/fwe..sdfv....\n", "output": "0\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "3\nhttp://abacaba.com/test\nhttp://abacaba.de/test\nhttp://abacaba.de/test\n", "output": "1\nhttp://abacaba.com http://abacaba.de \n", "metadata": {"func_name": null}}]	livecodebench	deepcoder_0	0
Solve the following coding problem using the programming language python: Dreamoon loves summing up something for no reason. One day he obtains two integers a and b occasionally. He wants to calculate the sum of all nice integers. Positive integer x is called nice if $\operatorname{mod}(x, b) \neq 0$ and $\frac{\operatorname{div}(x, b)}{\operatorname{mod}(x, b)} = k$, where k is some integer number in range [1, a]. By $\operatorname{div}(x, y)$ we denote the quotient of integer division of x and y. By $\operatorname{mod}(x, y)$ we denote the remainder of integer division of x and y. You can read more about these operations here: http://goo.gl/AcsXhT. The answer may be large, so please print its remainder modulo 1 000 000 007 (10^9 + 7). Can you compute it faster than Dreamoon? -----Input----- The single line of the input contains two integers a, b (1 ≤ a, b ≤ 10^7). -----Output----- Print a single integer representing the answer modulo 1 000 000 007 (10^9 + 7). -----Examples----- Input 1 1 Output 0 Input 2 2 Output 8 -----Note----- For the first sample, there are no nice integers because $\operatorname{mod}(x, 1)$ is always zero. For the second sample, the set of nice integers is {3, 5}. The input will be stdin and you should print your solution to stdout Now solve the problem and return the code.	[ "```python\na,b=map(int,input().split())\nprint(((b-1)ab//2+(a+1)abb(b-1)//4)%1000000007)\n```" ]	[{"type": "stdin_stdout", "input": "1 1\n", "output": "0\n"}, {"type": "stdin_stdout", "input": "2 2\n", "output": "8\n"}, {"type": "stdin_stdout", "input": "4 1\n", "output": "0\n"}, {"type": "stdin_stdout", "input": "4 2\n", "output": "24\n"}, {"type": "stdin_stdout", "input": "4 3\n", "output": "102\n"}, {"type": "stdin_stdout", "input": "4 4\n", "output": "264\n"}, {"type": "stdin_stdout", "input": "3 4\n", "output": "162\n"}, {"type": "stdin_stdout", "input": "2 4\n", "output": "84\n"}, {"type": "stdin_stdout", "input": "1 4\n", "output": "30\n"}, {"type": "stdin_stdout", "input": "1000 1000\n", "output": "247750000\n"}, {"type": "stdin_stdout", "input": "10000000 10000000\n", "output": "425362313\n"}, {"type": "stdin_stdout", "input": "10000000 9999999\n", "output": "930564389\n"}, {"type": "stdin_stdout", "input": "2 10000000\n", "output": "990423507\n"}, {"type": "stdin_stdout", "input": "10000000 2\n", "output": "19300000\n"}, {"type": "stdin_stdout", "input": "9999999 2\n", "output": "999300006\n"}, {"type": "stdin_stdout", "input": "9999999 9999999\n", "output": "957764103\n"}, {"type": "stdin_stdout", "input": "10000000 10000\n", "output": "723127969\n"}, {"type": "stdin_stdout", "input": "10000 10000000\n", "output": "372369289\n"}, {"type": "stdin_stdout", "input": "2 9999999\n", "output": "48573499\n"}, {"type": "stdin_stdout", "input": "123456 123456\n", "output": "417111819\n"}, {"type": "stdin_stdout", "input": "6407688 3000816\n", "output": "895399645\n"}, {"type": "stdin_stdout", "input": "9956532 1084240\n", "output": "554368769\n"}, {"type": "stdin_stdout", "input": "3505377 9167664\n", "output": "80435138\n"}, {"type": "stdin_stdout", "input": "7054221 7251088\n", "output": "7849970\n"}, {"type": "stdin_stdout", "input": "346169 367216\n", "output": "358144298\n"}, {"type": "stdin_stdout", "input": "3895014 8450640\n", "output": "627604019\n"}, {"type": "stdin_stdout", "input": "861392 6200826\n", "output": "180835815\n"}, {"type": "stdin_stdout", "input": "4410236 9316955\n", "output": "602743722\n"}, {"type": "stdin_stdout", "input": "2926377 2367675\n", "output": "395740917\n"}, {"type": "stdin_stdout", "input": "1507925 5483803\n", "output": "727607740\n"}, {"type": "stdin_stdout", "input": "9832578 8599931\n", "output": "428281878\n"}, {"type": "stdin_stdout", "input": "8348718 6683355\n", "output": "275994807\n"}, {"type": "stdin_stdout", "input": "1897562 4766779\n", "output": "148050609\n"}, {"type": "stdin_stdout", "input": "413703 2850203\n", "output": "76966774\n"}, {"type": "stdin_stdout", "input": "8995251 5966331\n", "output": "451718548\n"}, {"type": "stdin_stdout", "input": "7319903 9017051\n", "output": "975259203\n"}, {"type": "stdin_stdout", "input": "9253578 1799941\n", "output": "868664771\n"}, {"type": "stdin_stdout", "input": "7835126 9883365\n", "output": "119844544\n"}, {"type": "stdin_stdout", "input": "6351267 7966789\n", "output": "683811063\n"}, {"type": "stdin_stdout", "input": "9900111 1082917\n", "output": "539539383\n"}, {"type": "stdin_stdout", "input": "1 10000000\n", "output": "995024507\n"}, {"type": "stdin_stdout", "input": "123456 234567\n", "output": "93010021\n"}, {"type": "stdin_stdout", "input": "888888 888888\n", "output": "456888843\n"}, {"type": "stdin_stdout", "input": "1001 1500126\n", "output": "45074025\n"}, {"type": "stdin_stdout", "input": "9243243 432434\n", "output": "203891513\n"}, {"type": "stdin_stdout", "input": "3 10000000\n", "output": "986197007\n"}, {"type": "stdin_stdout", "input": "4108931 211273\n", "output": "142398939\n"}, {"type": "stdin_stdout", "input": "999999 92321\n", "output": "286549418\n"}, {"type": "stdin_stdout", "input": "999999 999999\n", "output": "691690639\n"}, {"type": "stdin_stdout", "input": "191919 123123\n", "output": "358196438\n"}, {"type": "stdin_stdout", "input": "999999 1000000\n", "output": "725921292\n"}, {"type": "stdin_stdout", "input": "31623 10000000\n", "output": "382702377\n"}, {"type": "stdin_stdout", "input": "1000023 1000043\n", "output": "175442768\n"}, {"type": "stdin_stdout", "input": "666666 666666\n", "output": "869302791\n"}, {"type": "stdin_stdout", "input": "7672285 753250\n", "output": "461773059\n"}, {"type": "stdin_stdout", "input": "1000000 1000000\n", "output": "249917764\n"}, {"type": "stdin_stdout", "input": "6340794 6874449\n", "output": "930977735\n"}, {"type": "stdin_stdout", "input": "9998486 9998486\n", "output": "988877388\n"}, {"type": "stdin_stdout", "input": "9999997 9999998\n", "output": "946983076\n"}]	null	null	You are an expert Python programmer. You will be given a question (problem specification) and will generate a correct Python program that matches the specification and passes all tests. Solve the following coding problem using the programming language python: Dreamoon loves summing up something for no reason. One day he obtains two integers a and b occasionally. He wants to calculate the sum of all nice integers. Positive integer x is called nice if $\operatorname{mod}(x, b) \neq 0$ and $\frac{\operatorname{div}(x, b)}{\operatorname{mod}(x, b)} = k$, where k is some integer number in range [1, a]. By $\operatorname{div}(x, y)$ we denote the quotient of integer division of x and y. By $\operatorname{mod}(x, y)$ we denote the remainder of integer division of x and y. You can read more about these operations here: http://goo.gl/AcsXhT. The answer may be large, so please print its remainder modulo 1 000 000 007 (10^9 + 7). Can you compute it faster than Dreamoon? -----Input----- The single line of the input contains two integers a, b (1 ≤ a, b ≤ 10^7). -----Output----- Print a single integer representing the answer modulo 1 000 000 007 (10^9 + 7). -----Examples----- Input 1 1 Output 0 Input 2 2 Output 8 -----Note----- For the first sample, there are no nice integers because $\operatorname{mod}(x, 1)$ is always zero. For the second sample, the set of nice integers is {3, 5}. The input will be stdin and you should print your solution to stdout Now solve the problem and return the code.### Format: Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within delimiters as follows. Ensure that when the python program runs, it reads the inputs, runs the algorithm and writes output to STDOUT. ```python # YOUR CODE HERE ``` ### Answer: (use the provided format with backticks)	[{"type": "stdin_stdout", "input": "1 1\n", "output": "0\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "2 2\n", "output": "8\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "4 1\n", "output": "0\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "4 2\n", "output": "24\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "4 3\n", "output": "102\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "4 4\n", "output": "264\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "3 4\n", "output": "162\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "2 4\n", "output": "84\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "1 4\n", 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null}}, {"type": "stdin_stdout", "input": "9243243 432434\n", "output": "203891513\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "3 10000000\n", "output": "986197007\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "4108931 211273\n", "output": "142398939\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "999999 92321\n", "output": "286549418\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "999999 999999\n", "output": "691690639\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "191919 123123\n", "output": "358196438\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "999999 1000000\n", "output": "725921292\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "31623 10000000\n", "output": "382702377\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "1000023 1000043\n", "output": "175442768\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "666666 666666\n", "output": "869302791\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "7672285 753250\n", "output": "461773059\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "1000000 1000000\n", "output": "249917764\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "6340794 6874449\n", "output": "930977735\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "9998486 9998486\n", "output": "988877388\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "9999997 9999998\n", "output": "946983076\n", "metadata": {"func_name": null}}]	livecodebench	deepcoder_1	1
Solve the following coding problem using the programming language python: Tavak and Seyyed are good friends. Seyyed is very funny and he told Tavak to solve the following problem instead of longest-path. You are given l and r. For all integers from l to r, inclusive, we wrote down all of their integer divisors except 1. Find the integer that we wrote down the maximum number of times. Solve the problem to show that it's not a NP problem. -----Input----- The first line contains two integers l and r (2 ≤ l ≤ r ≤ 10^9). -----Output----- Print single integer, the integer that appears maximum number of times in the divisors. If there are multiple answers, print any of them. -----Examples----- Input 19 29 Output 2 Input 3 6 Output 3 -----Note----- Definition of a divisor: https://www.mathsisfun.com/definitions/divisor-of-an-integer-.html The first example: from 19 to 29 these numbers are divisible by 2: {20, 22, 24, 26, 28}. The second example: from 3 to 6 these numbers are divisible by 3: {3, 6}. The input will be stdin and you should print your solution to stdout Now solve the problem and return the code.	[ "```python\nl,r = map(int, input().split(\" \"))\nif l == r:\n print (l)\nelse:\n print (2)\n```" ]	[{"type": "stdin_stdout", "input": "19 29\n", "output": "2\n"}, {"type": "stdin_stdout", "input": "3 6\n", "output": "2\n"}, {"type": "stdin_stdout", "input": "39 91\n", "output": "2\n"}, {"type": "stdin_stdout", "input": "76 134\n", "output": "2\n"}, {"type": "stdin_stdout", "input": "93 95\n", "output": "2\n"}, {"type": "stdin_stdout", "input": "17 35\n", "output": "2\n"}, {"type": "stdin_stdout", "input": "94 95\n", "output": "2\n"}, {"type": "stdin_stdout", "input": "51 52\n", "output": "2\n"}, {"type": "stdin_stdout", "input": "47 52\n", "output": "2\n"}, {"type": "stdin_stdout", "input": "38 98\n", "output": "2\n"}, {"type": "stdin_stdout", "input": "30 37\n", "output": "2\n"}, {"type": "stdin_stdout", "input": "56 92\n", "output": "2\n"}, {"type": "stdin_stdout", "input": "900000000 1000000000\n", "output": "2\n"}, {"type": "stdin_stdout", "input": "37622224 162971117\n", 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"1200007 1200007\n", "output": "1200007\n"}, {"type": "stdin_stdout", "input": "3 1000000000\n", "output": "2\n"}, {"type": "stdin_stdout", "input": "990000023 990000023\n", "output": "990000023\n"}, {"type": "stdin_stdout", "input": "1717 1717\n", "output": "1717\n"}, {"type": "stdin_stdout", "input": "141650963 141650963\n", "output": "141650963\n"}, {"type": "stdin_stdout", "input": "1002523 1002523\n", "output": "1002523\n"}, {"type": "stdin_stdout", "input": "900000011 900000011\n", "output": "900000011\n"}, {"type": "stdin_stdout", "input": "104729 104729\n", "output": "104729\n"}, {"type": "stdin_stdout", "input": "4 12\n", "output": "2\n"}, {"type": "stdin_stdout", "input": "100003 100003\n", "output": "100003\n"}, {"type": "stdin_stdout", "input": "17 17\n", "output": "17\n"}, {"type": "stdin_stdout", "input": "10 100\n", "output": "2\n"}]	null	null	You are an expert Python programmer. You will be given a question (problem specification) and will generate a correct Python program that matches the specification and passes all tests. Solve the following coding problem using the programming language python: Tavak and Seyyed are good friends. Seyyed is very funny and he told Tavak to solve the following problem instead of longest-path. You are given l and r. For all integers from l to r, inclusive, we wrote down all of their integer divisors except 1. Find the integer that we wrote down the maximum number of times. Solve the problem to show that it's not a NP problem. -----Input----- The first line contains two integers l and r (2 ≤ l ≤ r ≤ 10^9). -----Output----- Print single integer, the integer that appears maximum number of times in the divisors. If there are multiple answers, print any of them. -----Examples----- Input 19 29 Output 2 Input 3 6 Output 3 -----Note----- Definition of a divisor: https://www.mathsisfun.com/definitions/divisor-of-an-integer-.html The first example: from 19 to 29 these numbers are divisible by 2: {20, 22, 24, 26, 28}. The second example: from 3 to 6 these numbers are divisible by 3: {3, 6}. The input will be stdin and you should print your solution to stdout Now solve the problem and return the code.### Format: Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within delimiters as follows. Ensure that when the python program runs, it reads the inputs, runs the algorithm and writes output to STDOUT. ```python # YOUR CODE HERE ``` ### Answer: (use the provided format with backticks)	[{"type": "stdin_stdout", "input": "19 29\n", "output": "2\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "3 6\n", "output": "2\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "39 91\n", "output": "2\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "76 134\n", "output": "2\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "93 95\n", "output": "2\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "17 35\n", "output": "2\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "94 95\n", "output": "2\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "51 52\n", "output": "2\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "47 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"output": "990000023\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "1717 1717\n", "output": "1717\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "141650963 141650963\n", "output": "141650963\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "1002523 1002523\n", "output": "1002523\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "900000011 900000011\n", "output": "900000011\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "104729 104729\n", "output": "104729\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "4 12\n", "output": "2\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "100003 100003\n", "output": "100003\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "17 17\n", "output": "17\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "10 100\n", "output": "2\n", "metadata": {"func_name": null}}]	livecodebench	deepcoder_2	2
Solve the following coding problem using the programming language python: "QAQ" is a word to denote an expression of crying. Imagine "Q" as eyes with tears and "A" as a mouth. Now Diamond has given Bort a string consisting of only uppercase English letters of length n. There is a great number of "QAQ" in the string (Diamond is so cute!). $8$ illustration by 猫屋 https://twitter.com/nekoyaliu Bort wants to know how many subsequences "QAQ" are in the string Diamond has given. Note that the letters "QAQ" don't have to be consecutive, but the order of letters should be exact. -----Input----- The only line contains a string of length n (1 ≤ n ≤ 100). It's guaranteed that the string only contains uppercase English letters. -----Output----- Print a single integer — the number of subsequences "QAQ" in the string. -----Examples----- Input QAQAQYSYIOIWIN Output 4 Input QAQQQZZYNOIWIN Output 3 -----Note----- In the first example there are 4 subsequences "QAQ": "QAQAQYSYIOIWIN", "QAQAQYSYIOIWIN", "QAQAQYSYIOIWIN", "QAQAQYSYIOIWIN". The input will be stdin and you should print your solution to stdout Now solve the problem and return the code.	[ "```python\ns=input()\nans = 0\nfor i in range(len(s)):\n if s[i] == 'A':\n ans += s[:i].count('Q') * s[i:].count('Q')\nprint(ans)\n```" ]	[{"type": "stdin_stdout", "input": "QAQAQYSYIOIWIN\n", "output": "4\n"}, {"type": "stdin_stdout", "input": "QAQQQZZYNOIWIN\n", "output": "3\n"}, {"type": "stdin_stdout", "input": "QA\n", "output": "0\n"}, {"type": "stdin_stdout", "input": "IAQVAQZLQBQVQFTQQQADAQJA\n", "output": "24\n"}, {"type": "stdin_stdout", "input": "QQAAQASGAYAAAAKAKAQIQEAQAIAAIAQQQQQ\n", "output": "378\n"}, {"type": "stdin_stdout", "input": "AMVFNFJIAVNQJWIVONQOAOOQSNQSONOASONAONQINAONAOIQONANOIQOANOQINAONOQINAONOXJCOIAQOAOQAQAQAQAQWWWAQQAQ\n", "output": "1077\n"}, {"type": "stdin_stdout", "input": "AAQQAXBQQBQQXBNQRJAQKQNAQNQVDQASAGGANQQQQTJFFQQQTQQA\n", "output": "568\n"}, {"type": "stdin_stdout", "input": "KAZXAVLPJQBQVQQQQQAPAQQGQTQVZQAAAOYA\n", "output": "70\n"}, {"type": "stdin_stdout", "input": "W\n", "output": "0\n"}, {"type": "stdin_stdout", "input": "DBA\n", 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"QAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQA\n", "output": "20825\n"}, {"type": "stdin_stdout", "input": "AQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQAQ\n", "output": "20825\n"}, {"type": "stdin_stdout", "input": "Q\n", "output": "0\n"}, {"type": "stdin_stdout", "input": "A\n", "output": "0\n"}, {"type": "stdin_stdout", "input": "FFF\n", "output": "0\n"}, {"type": "stdin_stdout", "input": "AAAAAA\n", "output": "0\n"}]	null	null	You are an expert Python programmer. You will be given a question (problem specification) and will generate a correct Python program that matches the specification and passes all tests. Solve the following coding problem using the programming language python: "QAQ" is a word to denote an expression of crying. Imagine "Q" as eyes with tears and "A" as a mouth. Now Diamond has given Bort a string consisting of only uppercase English letters of length n. There is a great number of "QAQ" in the string (Diamond is so cute!). $8$ illustration by 猫屋 https://twitter.com/nekoyaliu Bort wants to know how many subsequences "QAQ" are in the string Diamond has given. Note that the letters "QAQ" don't have to be consecutive, but the order of letters should be exact. -----Input----- The only line contains a string of length n (1 ≤ n ≤ 100). It's guaranteed that the string only contains uppercase English letters. -----Output----- Print a single integer — the number of subsequences "QAQ" in the string. -----Examples----- Input QAQAQYSYIOIWIN Output 4 Input QAQQQZZYNOIWIN Output 3 -----Note----- In the first example there are 4 subsequences "QAQ": "QAQAQYSYIOIWIN", "QAQAQYSYIOIWIN", "QAQAQYSYIOIWIN", "QAQAQYSYIOIWIN". The input will be stdin and you should print your solution to stdout Now solve the problem and return the code.### Format: Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within delimiters as follows. Ensure that when the python program runs, it reads the inputs, runs the algorithm and writes output to STDOUT. ```python # YOUR CODE HERE ``` ### Answer: (use the provided format with backticks)	[{"type": "stdin_stdout", "input": "QAQAQYSYIOIWIN\n", "output": "4\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "QAQQQZZYNOIWIN\n", "output": "3\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "QA\n", "output": "0\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "IAQVAQZLQBQVQFTQQQADAQJA\n", "output": "24\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "QQAAQASGAYAAAAKAKAQIQEAQAIAAIAQQQQQ\n", "output": "378\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "AMVFNFJIAVNQJWIVONQOAOOQSNQSONOASONAONQINAONAOIQONANOIQOANOQINAONOQINAONOXJCOIAQOAOQAQAQAQAQWWWAQQAQ\n", "output": "1077\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": 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{"func_name": null}}, {"type": "stdin_stdout", "input": "AAAAAA\n", "output": "0\n", "metadata": {"func_name": null}}]	livecodebench	deepcoder_3	3
Solve the following coding problem using the programming language python: Codefortia is a small island country located somewhere in the West Pacific. It consists of $n$ settlements connected by $m$ bidirectional gravel roads. Curiously enough, the beliefs of the inhabitants require the time needed to pass each road to be equal either to $a$ or $b$ seconds. It's guaranteed that one can go between any pair of settlements by following a sequence of roads. Codefortia was recently struck by the financial crisis. Therefore, the king decided to abandon some of the roads so that: it will be possible to travel between each pair of cities using the remaining roads only, the sum of times required to pass each remaining road will be minimum possible (in other words, remaining roads must form minimum spanning tree, using the time to pass the road as its weight), among all the plans minimizing the sum of times above, the time required to travel between the king's residence (in settlement $1$) and the parliament house (in settlement $p$) using the remaining roads only will be minimum possible. The king, however, forgot where the parliament house was. For each settlement $p = 1, 2, \dots, n$, can you tell what is the minimum time required to travel between the king's residence and the parliament house (located in settlement $p$) after some roads are abandoned? -----Input----- The first line of the input contains four integers $n$, $m$, $a$ and $b$ ($2 \leq n \leq 70$, $n - 1 \leq m \leq 200$, $1 \leq a < b \leq 10^7$) — the number of settlements and gravel roads in Codefortia, and two possible travel times. Each of the following lines contains three integers $u, v, c$ ($1 \leq u, v \leq n$, $u \neq v$, $c \in \{a, b\}$) denoting a single gravel road between the settlements $u$ and $v$, which requires $c$ minutes to travel. You can assume that the road network is connected and has no loops or multiedges. -----Output----- Output a single line containing $n$ integers. The $p$-th of them should denote the minimum possible time required to travel from $1$ to $p$ after the selected roads are abandoned. Note that for each $p$ you can abandon a different set of roads. -----Examples----- Input 5 5 20 25 1 2 25 2 3 25 3 4 20 4 5 20 5 1 20 Output 0 25 60 40 20 Input 6 7 13 22 1 2 13 2 3 13 1 4 22 3 4 13 4 5 13 5 6 13 6 1 13 Output 0 13 26 39 26 13 -----Note----- The minimum possible sum of times required to pass each road in the first example is $85$ — exactly one of the roads with passing time $25$ must be abandoned. Note that after one of these roads is abandoned, it's now impossible to travel between settlements $1$ and $3$ in time $50$. The input will be stdin and you should print your solution to stdout Now solve the problem and return the code.	[ "```python\nimport heapq\nn,m,a,b=map(int,input().split())\ngraph={i:[] for i in range(n)}\nfor i in range(m):\n u,v,w=map(int,input().split())\n graph[u-1].append((v-1,w))\n graph[v-1].append((u-1,w))\ncomponents=[-1]n\ncomp=-1\nfor i in range(n):\n if components[i]==-1:\n comp+=1\n components[i]=comp\n prev=[]\n layer=[i]\n while layer!=[]:\n newlayer=[]\n for guy in layer:\n for guy1 in graph[guy]:\n if guy1[1]==a and components[guy1[0]]==-1:\n newlayer.append(guy1[0])\n components[guy1[0]]=comp\n prev=layer[:]\n layer=newlayer[:]\nuseless=[]\nfor guy in graph:\n for neigh in graph[guy]:\n if components[guy]==components[neigh[0]] and neigh[1]==b:\n useless.append((guy,neigh))\nfor guy in useless:\n graph[guy[0]].remove(guy[1])\ncounts=[0](comp+1)\nfor i in range(n):\n counts[components[i]]+=1\nbad=[]\nfor i in range(comp+1):\n if counts[i]<=3:\n bad.append(i)\n for j in range(n):\n if components[j]==i:\n components[j]=-1\nfor guy in bad[::-1]:\n for i in range(n):\n if components[i]>guy:\n components[i]-=1\ncomp-=len(bad)\ncomp+=1\ndists=[[float(\"inf\") for i in range(2*comp)] for j in range(n)]\ndists[0][0]=0\npq=[]\nheapq.heappush(pq,[0,0,0])\nremaining=n\nvisited=[0]n\nwhile len(pq)>0 and remaining>0:\n dist,vert,mask=heapq.heappop(pq)\n if visited[vert]==0:\n visited[vert]=1\n remaining-=1\n for neigh in graph[vert]:\n if neigh[1]==b:\n if components[vert]==components[neigh[0]] and components[vert]!=-1:\n continue\n if components[neigh[0]]!=-1:\n if mask & (2components[neigh[0]])>0:\n continue\n if components[vert]!=-1:\n maskn=mask+2(components[vert])\n else:\n maskn=mask\n else:\n maskn=mask\n if dist+neigh[1]<dists[neigh[0]][maskn]:\n dists[neigh[0]][maskn]=dist+neigh[1]\n heapq.heappush(pq,[dist+neigh[1],neigh[0],maskn])\noptimal=[str(min(dists[i])) for i in range(n)]\nprint(\" \".join(optimal))\n```" ]	[{"type": "stdin_stdout", "input": "5 5 20 25\n1 2 25\n2 3 25\n3 4 20\n4 5 20\n5 1 20\n", "output": "0 25 60 40 20\n"}, {"type": "stdin_stdout", "input": "6 7 13 22\n1 2 13\n2 3 13\n1 4 22\n3 4 13\n4 5 13\n5 6 13\n6 1 13\n", "output": "0 13 26 39 26 13\n"}, {"type": "stdin_stdout", "input": "2 1 1 2\n2 1 1\n", "output": "0 1\n"}, {"type": "stdin_stdout", "input": "2 1 9999999 10000000\n1 2 10000000\n", "output": "0 10000000\n"}, {"type": "stdin_stdout", "input": "3 3 78422 6789101\n3 1 6789101\n2 1 78422\n2 3 78422\n", "output": "0 78422 156844\n"}, {"type": "stdin_stdout", "input": "3 3 2770628 3912422\n1 2 2770628\n2 3 2770628\n1 3 3912422\n", "output": "0 2770628 5541256\n"}, {"type": "stdin_stdout", "input": "3 3 2566490 5132980\n1 2 2566490\n2 3 2566490\n3 1 5132980\n", "output": "0 2566490 5132980\n"}, {"type": "stdin_stdout", "input": "3 2 509529 5982470\n1 2 509529\n3 2 509529\n", "output": "0 509529 1019058\n"}, {"type": "stdin_stdout", "input": "3 2 1349740 8457492\n2 1 1349740\n3 1 1349740\n", "output": "0 1349740 1349740\n"}, {"type": "stdin_stdout", "input": "3 2 150319 5002968\n3 2 150319\n1 2 5002968\n", "output": "0 5002968 5153287\n"}, {"type": "stdin_stdout", "input": "3 2 990530 8623767\n3 2 8623767\n1 2 990530\n", "output": "0 990530 9614297\n"}, {"type": "stdin_stdout", "input": "3 2 810925 2022506\n1 2 2022506\n1 3 810925\n", "output": "0 2022506 810925\n"}, {"type": "stdin_stdout", "input": "3 2 1651136 5131013\n1 2 5131013\n3 2 5131013\n", "output": "0 5131013 10262026\n"}, {"type": "stdin_stdout", "input": "3 2 451715 1577270\n1 3 1577270\n1 2 1577270\n", "output": "0 1577270 1577270\n"}, {"type": "stdin_stdout", "input": "3 3 1291926 4943478\n2 3 1291926\n1 2 1291926\n3 1 1291926\n", "output": "0 1291926 1291926\n"}, {"type": "stdin_stdout", "input": "3 3 2132137 9084127\n1 2 2132137\n3 2 9084127\n3 1 2132137\n", "output": "0 2132137 2132137\n"}, {"type": "stdin_stdout", "input": "3 3 1126640 9858678\n3 1 9858678\n3 2 1126640\n1 2 9858678\n", "output": "0 9858678 9858678\n"}, {"type": "stdin_stdout", "input": "3 3 1966851 6439891\n1 3 6439891\n1 2 1966851\n3 2 6439891\n", "output": "0 1966851 6439891\n"}, {"type": "stdin_stdout", "input": "3 3 1787246 7806211\n3 2 7806211\n2 1 7806211\n1 3 7806211\n", "output": "0 7806211 7806211\n"}]	null	null	You are an expert Python programmer. You will be given a question (problem specification) and will generate a correct Python program that matches the specification and passes all tests. Solve the following coding problem using the programming language python: Codefortia is a small island country located somewhere in the West Pacific. It consists of $n$ settlements connected by $m$ bidirectional gravel roads. Curiously enough, the beliefs of the inhabitants require the time needed to pass each road to be equal either to $a$ or $b$ seconds. It's guaranteed that one can go between any pair of settlements by following a sequence of roads. Codefortia was recently struck by the financial crisis. Therefore, the king decided to abandon some of the roads so that: it will be possible to travel between each pair of cities using the remaining roads only, the sum of times required to pass each remaining road will be minimum possible (in other words, remaining roads must form minimum spanning tree, using the time to pass the road as its weight), among all the plans minimizing the sum of times above, the time required to travel between the king's residence (in settlement $1$) and the parliament house (in settlement $p$) using the remaining roads only will be minimum possible. The king, however, forgot where the parliament house was. For each settlement $p = 1, 2, \dots, n$, can you tell what is the minimum time required to travel between the king's residence and the parliament house (located in settlement $p$) after some roads are abandoned? -----Input----- The first line of the input contains four integers $n$, $m$, $a$ and $b$ ($2 \leq n \leq 70$, $n - 1 \leq m \leq 200$, $1 \leq a < b \leq 10^7$) — the number of settlements and gravel roads in Codefortia, and two possible travel times. Each of the following lines contains three integers $u, v, c$ ($1 \leq u, v \leq n$, $u \neq v$, $c \in \{a, b\}$) denoting a single gravel road between the settlements $u$ and $v$, which requires $c$ minutes to travel. You can assume that the road network is connected and has no loops or multiedges. -----Output----- Output a single line containing $n$ integers. The $p$-th of them should denote the minimum possible time required to travel from $1$ to $p$ after the selected roads are abandoned. Note that for each $p$ you can abandon a different set of roads. -----Examples----- Input 5 5 20 25 1 2 25 2 3 25 3 4 20 4 5 20 5 1 20 Output 0 25 60 40 20 Input 6 7 13 22 1 2 13 2 3 13 1 4 22 3 4 13 4 5 13 5 6 13 6 1 13 Output 0 13 26 39 26 13 -----Note----- The minimum possible sum of times required to pass each road in the first example is $85$ — exactly one of the roads with passing time $25$ must be abandoned. Note that after one of these roads is abandoned, it's now impossible to travel between settlements $1$ and $3$ in time $50$. The input will be stdin and you should print your solution to stdout Now solve the problem and return the code.### Format: Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within delimiters as follows. Ensure that when the python program runs, it reads the inputs, runs the algorithm and writes output to STDOUT. ```python # YOUR CODE HERE ``` ### Answer: (use the provided format with backticks)	[{"type": "stdin_stdout", "input": "5 5 20 25\n1 2 25\n2 3 25\n3 4 20\n4 5 20\n5 1 20\n", "output": "0 25 60 40 20\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "6 7 13 22\n1 2 13\n2 3 13\n1 4 22\n3 4 13\n4 5 13\n5 6 13\n6 1 13\n", "output": "0 13 26 39 26 13\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "2 1 1 2\n2 1 1\n", "output": "0 1\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "2 1 9999999 10000000\n1 2 10000000\n", "output": "0 10000000\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "3 3 78422 6789101\n3 1 6789101\n2 1 78422\n2 3 78422\n", "output": "0 78422 156844\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "3 3 2770628 3912422\n1 2 2770628\n2 3 2770628\n1 3 3912422\n", "output": "0 2770628 5541256\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "3 3 2566490 5132980\n1 2 2566490\n2 3 2566490\n3 1 5132980\n", "output": "0 2566490 5132980\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "3 2 509529 5982470\n1 2 509529\n3 2 509529\n", "output": "0 509529 1019058\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "3 2 1349740 8457492\n2 1 1349740\n3 1 1349740\n", "output": "0 1349740 1349740\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "3 2 150319 5002968\n3 2 150319\n1 2 5002968\n", "output": "0 5002968 5153287\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "3 2 990530 8623767\n3 2 8623767\n1 2 990530\n", "output": "0 990530 9614297\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "3 2 810925 2022506\n1 2 2022506\n1 3 810925\n", "output": "0 2022506 810925\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "3 2 1651136 5131013\n1 2 5131013\n3 2 5131013\n", "output": "0 5131013 10262026\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "3 2 451715 1577270\n1 3 1577270\n1 2 1577270\n", "output": "0 1577270 1577270\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "3 3 1291926 4943478\n2 3 1291926\n1 2 1291926\n3 1 1291926\n", "output": "0 1291926 1291926\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "3 3 2132137 9084127\n1 2 2132137\n3 2 9084127\n3 1 2132137\n", "output": "0 2132137 2132137\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "3 3 1126640 9858678\n3 1 9858678\n3 2 1126640\n1 2 9858678\n", "output": "0 9858678 9858678\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "3 3 1966851 6439891\n1 3 6439891\n1 2 1966851\n3 2 6439891\n", "output": "0 1966851 6439891\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "3 3 1787246 7806211\n3 2 7806211\n2 1 7806211\n1 3 7806211\n", "output": "0 7806211 7806211\n", "metadata": {"func_name": null}}]	livecodebench	deepcoder_4	4
Solve the following coding problem using the programming language python: Pikachu had an array with him. He wrote down all the non-empty subsequences of the array on paper. Note that an array of size n has 2^{n} - 1 non-empty subsequences in it. Pikachu being mischievous as he always is, removed all the subsequences in which Maximum_element_of_the_subsequence - Minimum_element_of_subsequence ≥ d Pikachu was finally left with X subsequences. However, he lost the initial array he had, and now is in serious trouble. He still remembers the numbers X and d. He now wants you to construct any such array which will satisfy the above conditions. All the numbers in the final array should be positive integers less than 10^18. Note the number of elements in the output array should not be more than 10^4. If no answer is possible, print - 1. -----Input----- The only line of input consists of two space separated integers X and d (1 ≤ X, d ≤ 10^9). -----Output----- Output should consist of two lines. First line should contain a single integer n (1 ≤ n ≤ 10 000)— the number of integers in the final array. Second line should consist of n space separated integers — a_1, a_2, ... , a_{n} (1 ≤ a_{i} < 10^18). If there is no answer, print a single integer -1. If there are multiple answers, print any of them. -----Examples----- Input 10 5 Output 6 5 50 7 15 6 100 Input 4 2 Output 4 10 100 1000 10000 -----Note----- In the output of the first example case, the remaining subsequences after removing those with Maximum_element_of_the_subsequence - Minimum_element_of_subsequence ≥ 5 are [5], [5, 7], [5, 6], [5, 7, 6], [50], [7], [7, 6], [15], [6], [100]. There are 10 of them. Hence, the array [5, 50, 7, 15, 6, 100] is valid. Similarly, in the output of the second example case, the remaining sub-sequences after removing those with Maximum_element_of_the_subsequence - Minimum_element_of_subsequence ≥ 2 are [10], [100], [1000], [10000]. There are 4 of them. Hence, the array [10, 100, 1000, 10000] is valid. The input will be stdin and you should print your solution to stdout Now solve the problem and return the code.	[ "```python\nX, D = list(map(int, input().split()))\ncn = 1\nadd0 = 1 if (X&1) else 0\nans = []\nfor i in range(30,0,-1):\n\tif not (X & (1<<i)): continue\n\tans += [cn]*i\n\tadd0 += 1\n\tcn += D\nfor i in range(add0):\n\tans.append(cn)\n\tcn += D\nprint(len(ans))\nprint(' '.join(map(str, ans)))\n\n```" ]	[{"type": "stdin_stdout", "input": "10 5\n", "output": "6\n1 1 1 7 13 19 "}, {"type": "stdin_stdout", "input": "4 2\n", "output": "3\n1 1 4 "}, {"type": "stdin_stdout", "input": "4 1\n", "output": "3\n1 1 3 "}, {"type": "stdin_stdout", "input": "1 1\n", "output": "1\n1 "}, {"type": "stdin_stdout", "input": "63 1\n", "output": "21\n1 1 1 1 1 3 3 3 3 5 5 5 7 7 9 11 13 15 17 19 21 "}, {"type": "stdin_stdout", "input": "98 88\n", "output": "15\n1 1 1 1 1 1 90 90 90 90 90 179 268 357 446 "}, {"type": "stdin_stdout", "input": "746 173\n", "output": "37\n1 1 1 1 1 1 1 1 1 175 175 175 175 175 175 175 349 349 349 349 349 349 523 523 523 523 523 697 697 697 871 1045 1219 1393 1567 1741 1915 "}, {"type": "stdin_stdout", "input": "890 553\n", "output": "43\n1 1 1 1 1 1 1 1 1 555 555 555 555 555 555 555 555 1109 1109 1109 1109 1109 1109 1663 1663 1663 1663 1663 2217 2217 2217 2217 2771 2771 2771 3325 3879 4433 4987 5541 6095 6649 7203 "}, {"type": "stdin_stdout", "input": "883 1000\n", "output": "40\n1 1 1 1 1 1 1 1 1 1002 1002 1002 1002 1002 1002 1002 1002 2003 2003 2003 2003 2003 2003 3004 3004 3004 3004 3004 4005 4005 4005 4005 5006 6007 7008 8009 9010 10011 11012 12013 "}, {"type": "stdin_stdout", "input": "1 1000\n", "output": "1\n1 "}, {"type": "stdin_stdout", "input": "695 188\n", "output": "35\n1 1 1 1 1 1 1 1 1 190 190 190 190 190 190 190 379 379 379 379 379 568 568 568 568 757 757 946 1135 1324 1513 1702 1891 2080 2269 "}, {"type": "stdin_stdout", "input": "2060 697\n", "output": "19\n1 1 1 1 1 1 1 1 1 1 1 699 699 699 1397 1397 2095 2793 3491 "}, {"type": "stdin_stdout", "input": "70 3321\n", "output": "12\n1 1 1 1 1 1 3323 3323 6645 9967 13289 16611 "}, {"type": "stdin_stdout", "input": "6358 1646\n", "output": "50\n1 1 1 1 1 1 1 1 1 1 1 1 1648 1648 1648 1648 1648 1648 1648 1648 1648 1648 1648 3295 3295 3295 3295 3295 3295 3295 4942 4942 4942 4942 4942 4942 6589 6589 6589 6589 8236 8236 9883 11530 13177 14824 16471 18118 19765 21412 "}, {"type": "stdin_stdout", "input": "15000 1\n", "output": "66\n1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 3 3 3 3 3 3 3 3 3 5 5 5 5 5 5 5 5 5 5 5 7 7 7 7 7 7 7 7 7 9 9 9 9 9 9 9 11 11 11 11 13 13 13 15 17 19 21 23 25 27 "}, {"type": "stdin_stdout", "input": "1048576 1\n", "output": "21\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 "}, {"type": "stdin_stdout", "input": "1000000 1\n", "output": "106\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 9 9 9 9 9 9 9 9 9 9 9 9 9 9 11 11 11 11 11 11 11 11 11 13 13 13 13 13 13 15 17 19 21 23 25 27 "}, {"type": "stdin_stdout", "input": "10009 1\n", "output": "54\n1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 3 3 3 3 3 3 3 5 5 5 5 5 5 5 5 5 7 7 7 7 7 7 7 7 9 9 9 9 11 11 11 13 15 17 19 21 23 25 "}, {"type": "stdin_stdout", "input": "10001 1\n", "output": "50\n1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 3 3 3 3 3 3 3 5 5 5 5 5 5 5 5 5 7 7 7 7 7 7 7 7 9 9 9 9 11 13 15 17 19 21 "}]	null	null	You are an expert Python programmer. You will be given a question (problem specification) and will generate a correct Python program that matches the specification and passes all tests. Solve the following coding problem using the programming language python: Pikachu had an array with him. He wrote down all the non-empty subsequences of the array on paper. Note that an array of size n has 2^{n} - 1 non-empty subsequences in it. Pikachu being mischievous as he always is, removed all the subsequences in which Maximum_element_of_the_subsequence - Minimum_element_of_subsequence ≥ d Pikachu was finally left with X subsequences. However, he lost the initial array he had, and now is in serious trouble. He still remembers the numbers X and d. He now wants you to construct any such array which will satisfy the above conditions. All the numbers in the final array should be positive integers less than 10^18. Note the number of elements in the output array should not be more than 10^4. If no answer is possible, print - 1. -----Input----- The only line of input consists of two space separated integers X and d (1 ≤ X, d ≤ 10^9). -----Output----- Output should consist of two lines. First line should contain a single integer n (1 ≤ n ≤ 10 000)— the number of integers in the final array. Second line should consist of n space separated integers — a_1, a_2, ... , a_{n} (1 ≤ a_{i} < 10^18). If there is no answer, print a single integer -1. If there are multiple answers, print any of them. -----Examples----- Input 10 5 Output 6 5 50 7 15 6 100 Input 4 2 Output 4 10 100 1000 10000 -----Note----- In the output of the first example case, the remaining subsequences after removing those with Maximum_element_of_the_subsequence - Minimum_element_of_subsequence ≥ 5 are [5], [5, 7], [5, 6], [5, 7, 6], [50], [7], [7, 6], [15], [6], [100]. There are 10 of them. Hence, the array [5, 50, 7, 15, 6, 100] is valid. Similarly, in the output of the second example case, the remaining sub-sequences after removing those with Maximum_element_of_the_subsequence - Minimum_element_of_subsequence ≥ 2 are [10], [100], [1000], [10000]. There are 4 of them. Hence, the array [10, 100, 1000, 10000] is valid. The input will be stdin and you should print your solution to stdout Now solve the problem and return the code.### Format: Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within delimiters as follows. Ensure that when the python program runs, it reads the inputs, runs the algorithm and writes output to STDOUT. ```python # YOUR CODE HERE ``` ### Answer: (use the provided format with backticks)	[{"type": "stdin_stdout", "input": "10 5\n", "output": "6\n1 1 1 7 13 19 ", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "4 2\n", "output": "3\n1 1 4 ", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "4 1\n", "output": "3\n1 1 3 ", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "1 1\n", "output": "1\n1 ", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "63 1\n", "output": "21\n1 1 1 1 1 3 3 3 3 5 5 5 7 7 9 11 13 15 17 19 21 ", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "98 88\n", "output": "15\n1 1 1 1 1 1 90 90 90 90 90 179 268 357 446 ", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "746 173\n", "output": "37\n1 1 1 1 1 1 1 1 1 175 175 175 175 175 175 175 349 349 349 349 349 349 523 523 523 523 523 697 697 697 871 1045 1219 1393 1567 1741 1915 ", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "890 553\n", "output": "43\n1 1 1 1 1 1 1 1 1 555 555 555 555 555 555 555 555 1109 1109 1109 1109 1109 1109 1663 1663 1663 1663 1663 2217 2217 2217 2217 2771 2771 2771 3325 3879 4433 4987 5541 6095 6649 7203 ", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "883 1000\n", "output": "40\n1 1 1 1 1 1 1 1 1 1002 1002 1002 1002 1002 1002 1002 1002 2003 2003 2003 2003 2003 2003 3004 3004 3004 3004 3004 4005 4005 4005 4005 5006 6007 7008 8009 9010 10011 11012 12013 ", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "1 1000\n", "output": "1\n1 ", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "695 188\n", "output": "35\n1 1 1 1 1 1 1 1 1 190 190 190 190 190 190 190 379 379 379 379 379 568 568 568 568 757 757 946 1135 1324 1513 1702 1891 2080 2269 ", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "2060 697\n", "output": "19\n1 1 1 1 1 1 1 1 1 1 1 699 699 699 1397 1397 2095 2793 3491 ", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "70 3321\n", "output": "12\n1 1 1 1 1 1 3323 3323 6645 9967 13289 16611 ", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "6358 1646\n", "output": "50\n1 1 1 1 1 1 1 1 1 1 1 1 1648 1648 1648 1648 1648 1648 1648 1648 1648 1648 1648 3295 3295 3295 3295 3295 3295 3295 4942 4942 4942 4942 4942 4942 6589 6589 6589 6589 8236 8236 9883 11530 13177 14824 16471 18118 19765 21412 ", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "15000 1\n", "output": "66\n1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 3 3 3 3 3 3 3 3 3 5 5 5 5 5 5 5 5 5 5 5 7 7 7 7 7 7 7 7 7 9 9 9 9 9 9 9 11 11 11 11 13 13 13 15 17 19 21 23 25 27 ", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "1048576 1\n", "output": "21\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 ", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "1000000 1\n", "output": "106\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 9 9 9 9 9 9 9 9 9 9 9 9 9 9 11 11 11 11 11 11 11 11 11 13 13 13 13 13 13 15 17 19 21 23 25 27 ", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "10009 1\n", "output": "54\n1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 3 3 3 3 3 3 3 5 5 5 5 5 5 5 5 5 7 7 7 7 7 7 7 7 9 9 9 9 11 11 11 13 15 17 19 21 23 25 ", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "10001 1\n", "output": "50\n1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 3 3 3 3 3 3 3 5 5 5 5 5 5 5 5 5 7 7 7 7 7 7 7 7 9 9 9 9 11 13 15 17 19 21 ", "metadata": {"func_name": null}}]	livecodebench	deepcoder_5	5
Solve the following coding problem using the programming language python: Vasya and Kolya play a game with a string, using the following rules. Initially, Kolya creates a string s, consisting of small English letters, and uniformly at random chooses an integer k from a segment [0, len(s) - 1]. He tells Vasya this string s, and then shifts it k letters to the left, i. e. creates a new string t = s_{k} + 1s_{k} + 2... s_{n}s_1s_2... s_{k}. Vasya does not know the integer k nor the string t, but he wants to guess the integer k. To do this, he asks Kolya to tell him the first letter of the new string, and then, after he sees it, open one more letter on some position, which Vasya can choose. Vasya understands, that he can't guarantee that he will win, but he wants to know the probability of winning, if he plays optimally. He wants you to compute this probability. Note that Vasya wants to know the value of k uniquely, it means, that if there are at least two cyclic shifts of s that fit the information Vasya knowns, Vasya loses. Of course, at any moment of the game Vasya wants to maximize the probability of his win. -----Input----- The only string contains the string s of length l (3 ≤ l ≤ 5000), consisting of small English letters only. -----Output----- Print the only number — the answer for the problem. You answer is considered correct, if its absolute or relative error does not exceed 10^{ - 6}. Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if $\frac{\|a - b\|}{\operatorname{max}(1,\|b\|)} \leq 10^{-6}$ -----Examples----- Input technocup Output 1.000000000000000 Input tictictactac Output 0.333333333333333 Input bbaabaabbb Output 0.100000000000000 -----Note----- In the first example Vasya can always open the second letter after opening the first letter, and the cyclic shift is always determined uniquely. In the second example if the first opened letter of t is "t" or "c", then Vasya can't guess the shift by opening only one other letter. On the other hand, if the first letter is "i" or "a", then he can open the fourth letter and determine the shift uniquely. The input will be stdin and you should print your solution to stdout Now solve the problem and return the code.	[ "```python\nstr = input()\nl = len(str)\na = [0] * (2 * l)\npos = [[] for i in range(26)]\nfor i, c in enumerate(str):\n t = ord(c) - ord('a')\n a[i] = t\n a[i + l] = t\n pos[t].append(i)\nans = 0\nfor c in range(26):\n cur = 0\n for k in range(1, l):\n cnt = [0] * 26\n for i in pos[c]:\n cnt[a[i + k]] += 1\n cur = max(cur, len(list([x for x in cnt if x == 1])))\n ans += cur\nprint(ans / l)\n\n```" ]	[{"type": "stdin_stdout", "input": "technocup\n", "output": "1.000000000000000\n"}, {"type": "stdin_stdout", "input": "tictictactac\n", "output": "0.333333333333333\n"}, {"type": "stdin_stdout", "input": "bbaabaabbb\n", "output": "0.100000000000000\n"}, {"type": "stdin_stdout", "input": "cbbbbcaaca\n", "output": "0.800000000000000\n"}, {"type": "stdin_stdout", "input": "cadbcdddda\n", "output": "0.800000000000000\n"}, {"type": "stdin_stdout", "input": "bababbdaee\n", "output": "1.000000000000000\n"}, {"type": "stdin_stdout", "input": "fabbbhgedd\n", "output": "1.000000000000000\n"}, {"type": "stdin_stdout", "input": "gaejllebhn\n", "output": "1.000000000000000\n"}, {"type": "stdin_stdout", "input": "bbababaaababaabbbbbabbbbbbaaabbabaaaaabbbbbaaaabbbbabaabaabababbbabbabbabaaababbabbababaaaaabaaaabbb\n", "output": "0.000000000000000\n"}, {"type": "stdin_stdout", "input": "eaaebccaeacdecaedcaabbbdeebccdcdaabeeaeeaddbaabdccebecebbbbedbdcbbbbbbecbaddcddcccdcbbadbecddecedbba\n", "output": "0.080000000000000\n"}, {"type": "stdin_stdout", "input": "hcdhgcchbdhbeagdcfedgcbaffebgcbcccadeefacbhefgeadfgchabgeebegahfgegahbddedfhffeadcedadgfbeebhgfahhfb\n", "output": "0.450000000000000\n"}, {"type": "stdin_stdout", "input": "difhjdjbcdjedhiegagdejkbjfcdcdagdijdjajecbheiabfbjdgjdecfhdkgdbkcgcgakkiiggfkgcfadkjhiijkjacgejfhjge\n", "output": "0.840000000000000\n"}, {"type": "stdin_stdout", "input": "khjcoijiicdkdianmdolmadobdkcmgifdnffddnjehhbldlkjffknficdcmokfacioiegjedbmadjioomdacbodcajcmonmnlabo\n", "output": "0.960000000000000\n"}, {"type": "stdin_stdout", "input": "kpsaloedscghjeaqadfhmlibjepjafdomkkorinrpakondtnrnknbqarbejcenrlsbfgdbsdmkpphbkdnbitjfcofsjibssmmlll\n", "output": "1.000000000000000\n"}, {"type": "stdin_stdout", "input": "jkeaagakbifeaechkifkdghcjcgighidcgdccfbdbcackfgaebkddabgijkhjkaffkabacekdkjekeccegbecbkecbgbgcacgdackcdfjefaifgbigahkbedidfhjbikejdhejcgideaeejdcegeeccaefbddejkbdkfagfcdjbikbidfggkidcdcic\n", "output": "0.438502673796791\n"}, {"type": "stdin_stdout", "input": "ibledofnibedebifmnjdoaijeghajecbkjaebbkofnacceaodiifbhgkihkibddneeiemacodeafeaiiiaoajhmkjffbmmiehebhokfklhbkeoanoajdedjdlkbhenidclagggfhhhldfleccgmjbkhaginlhabkabagikalccndciokabfaebjkndf\n", "output": "0.786096256684492\n"}, {"type": "stdin_stdout", "input": "aaabbbaaaabbbbaaabbbbbaabbbbaaababbaaabbbbaaabbbbababbbbaaabbbbaaabbbbbaabbbbaaabbbbaaabbbb\n", "output": "0.000000000000000\n"}, {"type": "stdin_stdout", "input": "abbbaababbbaababbbaababbbaababbbaababbbaababbbaababbbaababbbaababbbaababbbaababbbaababbbaab\n", "output": "0.000000000000000\n"}, {"type": "stdin_stdout", "input": "abbacba\n", "output": "1.000000000000000\n"}]	null	null	You are an expert Python programmer. You will be given a question (problem specification) and will generate a correct Python program that matches the specification and passes all tests. Solve the following coding problem using the programming language python: Vasya and Kolya play a game with a string, using the following rules. Initially, Kolya creates a string s, consisting of small English letters, and uniformly at random chooses an integer k from a segment [0, len(s) - 1]. He tells Vasya this string s, and then shifts it k letters to the left, i. e. creates a new string t = s_{k} + 1s_{k} + 2... s_{n}s_1s_2... s_{k}. Vasya does not know the integer k nor the string t, but he wants to guess the integer k. To do this, he asks Kolya to tell him the first letter of the new string, and then, after he sees it, open one more letter on some position, which Vasya can choose. Vasya understands, that he can't guarantee that he will win, but he wants to know the probability of winning, if he plays optimally. He wants you to compute this probability. Note that Vasya wants to know the value of k uniquely, it means, that if there are at least two cyclic shifts of s that fit the information Vasya knowns, Vasya loses. Of course, at any moment of the game Vasya wants to maximize the probability of his win. -----Input----- The only string contains the string s of length l (3 ≤ l ≤ 5000), consisting of small English letters only. -----Output----- Print the only number — the answer for the problem. You answer is considered correct, if its absolute or relative error does not exceed 10^{ - 6}. Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if $\frac{\|a - b\|}{\operatorname{max}(1,\|b\|)} \leq 10^{-6}$ -----Examples----- Input technocup Output 1.000000000000000 Input tictictactac Output 0.333333333333333 Input bbaabaabbb Output 0.100000000000000 -----Note----- In the first example Vasya can always open the second letter after opening the first letter, and the cyclic shift is always determined uniquely. In the second example if the first opened letter of t is "t" or "c", then Vasya can't guess the shift by opening only one other letter. On the other hand, if the first letter is "i" or "a", then he can open the fourth letter and determine the shift uniquely. The input will be stdin and you should print your solution to stdout Now solve the problem and return the code.### Format: Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within delimiters as follows. Ensure that when the python program runs, it reads the inputs, runs the algorithm and writes output to STDOUT. ```python # YOUR CODE HERE ``` ### Answer: (use the provided format with backticks)	[{"type": "stdin_stdout", "input": "technocup\n", "output": "1.000000000000000\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "tictictactac\n", "output": "0.333333333333333\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "bbaabaabbb\n", "output": "0.100000000000000\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "cbbbbcaaca\n", "output": "0.800000000000000\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "cadbcdddda\n", "output": "0.800000000000000\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "bababbdaee\n", "output": "1.000000000000000\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "fabbbhgedd\n", "output": "1.000000000000000\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "gaejllebhn\n", "output": "1.000000000000000\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "bbababaaababaabbbbbabbbbbbaaabbabaaaaabbbbbaaaabbbbabaabaabababbbabbabbabaaababbabbababaaaaabaaaabbb\n", "output": "0.000000000000000\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "eaaebccaeacdecaedcaabbbdeebccdcdaabeeaeeaddbaabdccebecebbbbedbdcbbbbbbecbaddcddcccdcbbadbecddecedbba\n", "output": "0.080000000000000\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "hcdhgcchbdhbeagdcfedgcbaffebgcbcccadeefacbhefgeadfgchabgeebegahfgegahbddedfhffeadcedadgfbeebhgfahhfb\n", "output": "0.450000000000000\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "difhjdjbcdjedhiegagdejkbjfcdcdagdijdjajecbheiabfbjdgjdecfhdkgdbkcgcgakkiiggfkgcfadkjhiijkjacgejfhjge\n", "output": "0.840000000000000\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "khjcoijiicdkdianmdolmadobdkcmgifdnffddnjehhbldlkjffknficdcmokfacioiegjedbmadjioomdacbodcajcmonmnlabo\n", "output": "0.960000000000000\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "kpsaloedscghjeaqadfhmlibjepjafdomkkorinrpakondtnrnknbqarbejcenrlsbfgdbsdmkpphbkdnbitjfcofsjibssmmlll\n", "output": "1.000000000000000\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "jkeaagakbifeaechkifkdghcjcgighidcgdccfbdbcackfgaebkddabgijkhjkaffkabacekdkjekeccegbecbkecbgbgcacgdackcdfjefaifgbigahkbedidfhjbikejdhejcgideaeejdcegeeccaefbddejkbdkfagfcdjbikbidfggkidcdcic\n", "output": "0.438502673796791\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "ibledofnibedebifmnjdoaijeghajecbkjaebbkofnacceaodiifbhgkihkibddneeiemacodeafeaiiiaoajhmkjffbmmiehebhokfklhbkeoanoajdedjdlkbhenidclagggfhhhldfleccgmjbkhaginlhabkabagikalccndciokabfaebjkndf\n", "output": "0.786096256684492\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "aaabbbaaaabbbbaaabbbbbaabbbbaaababbaaabbbbaaabbbbababbbbaaabbbbaaabbbbbaabbbbaaabbbbaaabbbb\n", "output": "0.000000000000000\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "abbbaababbbaababbbaababbbaababbbaababbbaababbbaababbbaababbbaababbbaababbbaababbbaababbbaab\n", "output": "0.000000000000000\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "abbacba\n", "output": "1.000000000000000\n", "metadata": {"func_name": null}}]	livecodebench	deepcoder_6	6
Solve the following coding problem using the programming language python: In the evenings Donkey would join Shrek to look at the stars. They would sit on a log, sipping tea and they would watch the starry sky. The sky hung above the roof, right behind the chimney. Shrek's stars were to the right of the chimney and the Donkey's stars were to the left. Most days the Donkey would just count the stars, so he knew that they are exactly n. This time he wanted a challenge. He imagined a coordinate system: he put the origin of the coordinates at the intersection of the roof and the chimney, directed the OX axis to the left along the roof and the OY axis — up along the chimney (see figure). The Donkey imagined two rays emanating from he origin of axes at angles α_1 and α_2 to the OX axis. [Image] Now he chooses any star that lies strictly between these rays. After that he imagines more rays that emanate from this star at the same angles α_1 and α_2 to the OX axis and chooses another star that lies strictly between the new rays. He repeats the operation as long as there still are stars he can choose between the rays that emanate from a star. [Image] As a result, the Donkey gets a chain of stars. He can consecutively get to each star if he acts by the given rules. Your task is to find the maximum number of stars m that the Donkey's chain can contain. Note that the chain must necessarily start in the point of the origin of the axes, that isn't taken into consideration while counting the number m of stars in the chain. -----Input----- The first line contains an integer n (1 ≤ n ≤ 10^5) — the number of stars. The second line contains simple fractions representing relationships "a/b c/d", such that $\frac{a}{b} = \frac{\operatorname{sin} \alpha_{1}}{\operatorname{cos} \alpha_{1}}$ and $\frac{c}{d} = \frac{\operatorname{sin} \alpha_{2}}{\operatorname{cos} \alpha}$ (0 ≤ a, b, c, d ≤ 10^5; $0^{\circ} \leq \alpha_{1} < \alpha_{2} \leq 90^{\circ}$; $\frac{a}{b} \neq \frac{0}{0}$; $\frac{c}{d} \neq \frac{0}{0}$). The given numbers a, b, c, d are integers. Next n lines contain pairs of integers x_{i}, y_{i} (1 ≤ x_{i}, y_{i} ≤ 10^5)— the stars' coordinates. It is guaranteed that all stars have distinct coordinates. -----Output----- In a single line print number m — the answer to the problem. -----Examples----- Input 15 1/3 2/1 3 1 6 2 4 2 2 5 4 5 6 6 3 4 1 6 2 1 7 4 9 3 5 3 1 3 15 5 12 4 Output 4 -----Note----- In the sample the longest chain the Donkey can build consists of four stars. Note that the Donkey can't choose the stars that lie on the rays he imagines. [Image] The input will be stdin and you should print your solution to stdout Now solve the problem and return the code.	[ "```python\nfrom bisect import \nfrom math import \n\nn = int(input())\na, b, c, d = list(map(int,input().replace('/',' ').split()))\n\nalpha = atan2(c,d) - atan2(a,b)\ntan_alpha = tan(alpha)\n\nlis = []\n\nfor x,y in sorted((y/tan_alpha - x,y) for x,y in [ (x,y) for x,y in [(bx + ay,-ax + by) for x, y in [list(map(int,input().split())) for _ in range(n)] if ax - by <= 0 and dy - cx <= 0]]):\n pos = bisect_left(lis,-y)\n if pos == len(lis):\n lis.append(-y)\n else:\n lis[pos] = -y\n\nprint(len(lis))\n\n\n```" ]	[{"type": "stdin_stdout", "input": "15\n1/3 2/1\n3 1\n6 2\n4 2\n2 5\n4 5\n6 6\n3 4\n1 6\n2 1\n7 4\n9 3\n5 3\n1 3\n15 5\n12 4\n", "output": "4\n"}, {"type": "stdin_stdout", "input": "15\n2/1 2/0\n3 1\n6 2\n9 3\n12 4\n15 5\n2 1\n4 2\n5 3\n7 4\n1 3\n3 4\n2 5\n4 5\n1 6\n6 6\n", "output": "1\n"}, {"type": "stdin_stdout", "input": "15\n2/1 2/0\n3 1\n6 2\n9 3\n12 4\n15 5\n2 1\n4 2\n5 3\n7 4\n1 3\n3 4\n2 6\n4 5\n1 6\n6 6\n", "output": "2\n"}, {"type": "stdin_stdout", "input": "15\n1/4 2/1\n3 1\n6 2\n9 3\n12 4\n15 5\n2 1\n4 2\n5 3\n7 4\n1 3\n3 4\n2 5\n4 5\n1 6\n6 6\n", "output": "5\n"}, {"type": "stdin_stdout", "input": "5\n3/24 24/3\n31394 23366\n27990 71363\n33642 36903\n79731 10588\n10907 5058\n", "output": "3\n"}, {"type": "stdin_stdout", "input": "5\n3/18 18/17\n84697 26074\n16334 31084\n38824 37740\n1288 50582\n87807 48721\n", "output": "2\n"}, {"type": "stdin_stdout", "input": "5\n3/18 18/17\n5148 38615\n84759 63111\n16345 23100\n49727 20597\n43590 46573\n", "output": "1\n"}, {"type": "stdin_stdout", "input": "5\n3/18 18/17\n49797 95131\n5075 96918\n91898 7865\n91852 41070\n12076 45049\n", "output": "1\n"}, {"type": "stdin_stdout", "input": "5\n3/18 18/17\n43008 52460\n68903 46619\n16613 30280\n66639 17904\n83797 83401\n", "output": "1\n"}, {"type": "stdin_stdout", "input": "5\n3/18 18/17\n66980 84763\n69224 39\n62888 61748\n53474 234\n77487 94808\n", "output": "1\n"}, {"type": "stdin_stdout", "input": "5\n3/18 18/17\n35429 29897\n89928 67711\n29047 22691\n84838 6917\n32683 99009\n", "output": "2\n"}, {"type": "stdin_stdout", "input": "5\n3/18 18/17\n62344 72564\n31069 2824\n74485 34763\n61186 78544\n75470 51019\n", "output": "1\n"}, {"type": "stdin_stdout", "input": "5\n27/18 27/17\n27746 42830\n22071 47985\n44242 62799\n16038 48367\n85158 21622\n", "output": "1\n"}, {"type": "stdin_stdout", "input": "5\n27/18 27/17\n91659 76441\n96317 38081\n99805 94867\n79758 84753\n96445 53616\n", "output": "0\n"}, {"type": "stdin_stdout", "input": "5\n27/18 27/17\n85006 4046\n10811 30171\n97316 32923\n73899 71559\n76723 17949\n", "output": "0\n"}, {"type": "stdin_stdout", "input": "5\n0/17 74/0\n24922 93126\n75686 80827\n33683 91759\n10584 66980\n58159 52129\n", "output": "2\n"}, {"type": "stdin_stdout", "input": "5\n0/17 74/0\n69711 29703\n91677 56040\n26051 78244\n20816 40897\n70770 35908\n", "output": "3\n"}, {"type": "stdin_stdout", "input": "5\n0/17 74/0\n68877 18122\n96115 84747\n71027 43746\n31622 3444\n93281 34803\n", "output": "4\n"}, {"type": "stdin_stdout", "input": "5\n3/24 24/3\n31394 23366\n27990 71363\n33642 36903\n79731 10588\n10907 5058\n", "output": "3\n"}]	null	null	You are an expert Python programmer. You will be given a question (problem specification) and will generate a correct Python program that matches the specification and passes all tests. Solve the following coding problem using the programming language python: In the evenings Donkey would join Shrek to look at the stars. They would sit on a log, sipping tea and they would watch the starry sky. The sky hung above the roof, right behind the chimney. Shrek's stars were to the right of the chimney and the Donkey's stars were to the left. Most days the Donkey would just count the stars, so he knew that they are exactly n. This time he wanted a challenge. He imagined a coordinate system: he put the origin of the coordinates at the intersection of the roof and the chimney, directed the OX axis to the left along the roof and the OY axis — up along the chimney (see figure). The Donkey imagined two rays emanating from he origin of axes at angles α_1 and α_2 to the OX axis. [Image] Now he chooses any star that lies strictly between these rays. After that he imagines more rays that emanate from this star at the same angles α_1 and α_2 to the OX axis and chooses another star that lies strictly between the new rays. He repeats the operation as long as there still are stars he can choose between the rays that emanate from a star. [Image] As a result, the Donkey gets a chain of stars. He can consecutively get to each star if he acts by the given rules. Your task is to find the maximum number of stars m that the Donkey's chain can contain. Note that the chain must necessarily start in the point of the origin of the axes, that isn't taken into consideration while counting the number m of stars in the chain. -----Input----- The first line contains an integer n (1 ≤ n ≤ 10^5) — the number of stars. The second line contains simple fractions representing relationships "a/b c/d", such that $\frac{a}{b} = \frac{\operatorname{sin} \alpha_{1}}{\operatorname{cos} \alpha_{1}}$ and $\frac{c}{d} = \frac{\operatorname{sin} \alpha_{2}}{\operatorname{cos} \alpha}$ (0 ≤ a, b, c, d ≤ 10^5; $0^{\circ} \leq \alpha_{1} < \alpha_{2} \leq 90^{\circ}$; $\frac{a}{b} \neq \frac{0}{0}$; $\frac{c}{d} \neq \frac{0}{0}$). The given numbers a, b, c, d are integers. Next n lines contain pairs of integers x_{i}, y_{i} (1 ≤ x_{i}, y_{i} ≤ 10^5)— the stars' coordinates. It is guaranteed that all stars have distinct coordinates. -----Output----- In a single line print number m — the answer to the problem. -----Examples----- Input 15 1/3 2/1 3 1 6 2 4 2 2 5 4 5 6 6 3 4 1 6 2 1 7 4 9 3 5 3 1 3 15 5 12 4 Output 4 -----Note----- In the sample the longest chain the Donkey can build consists of four stars. Note that the Donkey can't choose the stars that lie on the rays he imagines. [Image] The input will be stdin and you should print your solution to stdout Now solve the problem and return the code.### Format: Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within delimiters as follows. Ensure that when the python program runs, it reads the inputs, runs the algorithm and writes output to STDOUT. ```python # YOUR CODE HERE ``` ### Answer: (use the provided format with backticks)	[{"type": "stdin_stdout", "input": "15\n1/3 2/1\n3 1\n6 2\n4 2\n2 5\n4 5\n6 6\n3 4\n1 6\n2 1\n7 4\n9 3\n5 3\n1 3\n15 5\n12 4\n", "output": "4\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "15\n2/1 2/0\n3 1\n6 2\n9 3\n12 4\n15 5\n2 1\n4 2\n5 3\n7 4\n1 3\n3 4\n2 5\n4 5\n1 6\n6 6\n", "output": "1\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "15\n2/1 2/0\n3 1\n6 2\n9 3\n12 4\n15 5\n2 1\n4 2\n5 3\n7 4\n1 3\n3 4\n2 6\n4 5\n1 6\n6 6\n", "output": "2\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "15\n1/4 2/1\n3 1\n6 2\n9 3\n12 4\n15 5\n2 1\n4 2\n5 3\n7 4\n1 3\n3 4\n2 5\n4 5\n1 6\n6 6\n", "output": "5\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "5\n3/24 24/3\n31394 23366\n27990 71363\n33642 36903\n79731 10588\n10907 5058\n", "output": "3\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "5\n3/18 18/17\n84697 26074\n16334 31084\n38824 37740\n1288 50582\n87807 48721\n", "output": "2\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "5\n3/18 18/17\n5148 38615\n84759 63111\n16345 23100\n49727 20597\n43590 46573\n", "output": "1\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "5\n3/18 18/17\n49797 95131\n5075 96918\n91898 7865\n91852 41070\n12076 45049\n", "output": "1\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "5\n3/18 18/17\n43008 52460\n68903 46619\n16613 30280\n66639 17904\n83797 83401\n", "output": "1\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "5\n3/18 18/17\n66980 84763\n69224 39\n62888 61748\n53474 234\n77487 94808\n", "output": "1\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "5\n3/18 18/17\n35429 29897\n89928 67711\n29047 22691\n84838 6917\n32683 99009\n", "output": "2\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "5\n3/18 18/17\n62344 72564\n31069 2824\n74485 34763\n61186 78544\n75470 51019\n", "output": "1\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "5\n27/18 27/17\n27746 42830\n22071 47985\n44242 62799\n16038 48367\n85158 21622\n", "output": "1\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "5\n27/18 27/17\n91659 76441\n96317 38081\n99805 94867\n79758 84753\n96445 53616\n", "output": "0\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "5\n27/18 27/17\n85006 4046\n10811 30171\n97316 32923\n73899 71559\n76723 17949\n", "output": "0\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "5\n0/17 74/0\n24922 93126\n75686 80827\n33683 91759\n10584 66980\n58159 52129\n", "output": "2\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "5\n0/17 74/0\n69711 29703\n91677 56040\n26051 78244\n20816 40897\n70770 35908\n", "output": "3\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "5\n0/17 74/0\n68877 18122\n96115 84747\n71027 43746\n31622 3444\n93281 34803\n", "output": "4\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "5\n3/24 24/3\n31394 23366\n27990 71363\n33642 36903\n79731 10588\n10907 5058\n", "output": "3\n", "metadata": {"func_name": null}}]	livecodebench	deepcoder_7	7
Solve the following coding problem using the programming language python: The Little Elephant has an integer a, written in the binary notation. He wants to write this number on a piece of paper. To make sure that the number a fits on the piece of paper, the Little Elephant ought to delete exactly one any digit from number a in the binary record. At that a new number appears. It consists of the remaining binary digits, written in the corresponding order (possible, with leading zeroes). The Little Elephant wants the number he is going to write on the paper to be as large as possible. Help him find the maximum number that he can obtain after deleting exactly one binary digit and print it in the binary notation. -----Input----- The single line contains integer a, written in the binary notation without leading zeroes. This number contains more than 1 and at most 10^5 digits. -----Output----- In the single line print the number that is written without leading zeroes in the binary notation — the answer to the problem. -----Examples----- Input 101 Output 11 Input 110010 Output 11010 -----Note----- In the first sample the best strategy is to delete the second digit. That results in number 11_2 = 3_10. In the second sample the best strategy is to delete the third or fourth digits — that results in number 11010_2 = 26_10. The input will be stdin and you should print your solution to stdout Now solve the problem and return the code.	[ "```python\nx = input ()\n\nflag = 0\ns = 0\n\nfor each_item in x:\n if each_item == '0':\n if flag == 0:\n flag = 1;\n continue\n else:\n print (each_item, end = '')\n else:\n if (s == len (x) - 1 and flag == 0) :\n continue\n print (each_item, end = '')\n s = s + 1\n\n```" ]	[{"type": "stdin_stdout", "input": "101\n", "output": "11\n"}, {"type": "stdin_stdout", "input": "110010\n", "output": "11010\n"}, {"type": "stdin_stdout", "input": "10000\n", "output": "1000\n"}, {"type": "stdin_stdout", "input": "1111111110\n", "output": "111111111\n"}, {"type": "stdin_stdout", "input": "10100101011110101\n", "output": "1100101011110101\n"}, {"type": "stdin_stdout", "input": "111010010111\n", "output": "11110010111\n"}, {"type": "stdin_stdout", "input": "11110111011100000000\n", "output": "1111111011100000000\n"}, {"type": "stdin_stdout", "input": "11110010010100001110110101110011110110100111101\n", "output": "1111010010100001110110101110011110110100111101\n"}, {"type": "stdin_stdout", "input": "1001011111010010100111111\n", "output": "101011111010010100111111\n"}, {"type": "stdin_stdout", "input": "1111111111\n", "output": "111111111\n"}, {"type": "stdin_stdout", "input": "1111111111111111111100111101001110110111111000001111110101001101001110011000001011001111111000110101\n", "output": "111111111111111111110111101001110110111111000001111110101001101001110011000001011001111111000110101\n"}, {"type": "stdin_stdout", "input": "11010110000100100101111110111001001010011000011011000010010100111010101000111010011101101111110001111000101000001100011101110100\n", "output": "1110110000100100101111110111001001010011000011011000010010100111010101000111010011101101111110001111000101000001100011101110100\n"}, {"type": "stdin_stdout", "input": "11111111111111111111111110110111001101100111010010101101101001011100011011000111010011110010101100010001011101011010010100001000011100001101101001100010100001001010010100100001111110100110011000101100001111111011010111001011111110111101000100101001001011\n", "output": "1111111111111111111111111110111001101100111010010101101101001011100011011000111010011110010101100010001011101011010010100001000011100001101101001100010100001001010010100100001111110100110011000101100001111111011010111001011111110111101000100101001001011\n"}, {"type": "stdin_stdout", "input": "11100010010010000110101101101100111111001010001101101001001111010110010111001011010000001100110101000101111000001111101111110010000010101110011110101101010110001100011101111011100010011101100111110010111111100110101000000111101000000000110100100101111101000110101010101101001110001110000101011010101100011100100111100010001011010010001100011111110010011010011000111000100111100010110100011010010101011011011111110100001110000011011\n", "output": "1110010010010000110101101101100111111001010001101101001001111010110010111001011010000001100110101000101111000001111101111110010000010101110011110101101010110001100011101111011100010011101100111110010111111100110101000000111101000000000110100100101111101000110101010101101001110001110000101011010101100011100100111100010001011010010001100011111110010011010011000111000100111100010110100011010010101011011011111110100001110000011011\n"}, {"type": "stdin_stdout", "input": "11\n", "output": "1\n"}, {"type": "stdin_stdout", "input": "111\n", "output": "11\n"}, {"type": "stdin_stdout", "input": "111111\n", "output": "11111\n"}, {"type": "stdin_stdout", "input": "11111\n", "output": "1111\n"}, {"type": "stdin_stdout", "input": "1111\n", "output": "111\n"}]	null	null	You are an expert Python programmer. You will be given a question (problem specification) and will generate a correct Python program that matches the specification and passes all tests. Solve the following coding problem using the programming language python: The Little Elephant has an integer a, written in the binary notation. He wants to write this number on a piece of paper. To make sure that the number a fits on the piece of paper, the Little Elephant ought to delete exactly one any digit from number a in the binary record. At that a new number appears. It consists of the remaining binary digits, written in the corresponding order (possible, with leading zeroes). The Little Elephant wants the number he is going to write on the paper to be as large as possible. Help him find the maximum number that he can obtain after deleting exactly one binary digit and print it in the binary notation. -----Input----- The single line contains integer a, written in the binary notation without leading zeroes. This number contains more than 1 and at most 10^5 digits. -----Output----- In the single line print the number that is written without leading zeroes in the binary notation — the answer to the problem. -----Examples----- Input 101 Output 11 Input 110010 Output 11010 -----Note----- In the first sample the best strategy is to delete the second digit. That results in number 11_2 = 3_10. In the second sample the best strategy is to delete the third or fourth digits — that results in number 11010_2 = 26_10. The input will be stdin and you should print your solution to stdout Now solve the problem and return the code.### Format: Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within delimiters as follows. Ensure that when the python program runs, it reads the inputs, runs the algorithm and writes output to STDOUT. ```python # YOUR CODE HERE ``` ### Answer: (use the provided format with backticks)	[{"type": "stdin_stdout", "input": "101\n", "output": "11\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "110010\n", "output": "11010\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "10000\n", "output": "1000\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "1111111110\n", "output": "111111111\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "10100101011110101\n", "output": "1100101011110101\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "111010010111\n", "output": "11110010111\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "11110111011100000000\n", "output": "1111111011100000000\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "11110010010100001110110101110011110110100111101\n", "output": "1111010010100001110110101110011110110100111101\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "1001011111010010100111111\n", "output": "101011111010010100111111\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "1111111111\n", "output": "111111111\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "1111111111111111111100111101001110110111111000001111110101001101001110011000001011001111111000110101\n", "output": "111111111111111111110111101001110110111111000001111110101001101001110011000001011001111111000110101\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "11010110000100100101111110111001001010011000011011000010010100111010101000111010011101101111110001111000101000001100011101110100\n", "output": "1110110000100100101111110111001001010011000011011000010010100111010101000111010011101101111110001111000101000001100011101110100\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "11111111111111111111111110110111001101100111010010101101101001011100011011000111010011110010101100010001011101011010010100001000011100001101101001100010100001001010010100100001111110100110011000101100001111111011010111001011111110111101000100101001001011\n", "output": "1111111111111111111111111110111001101100111010010101101101001011100011011000111010011110010101100010001011101011010010100001000011100001101101001100010100001001010010100100001111110100110011000101100001111111011010111001011111110111101000100101001001011\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "11100010010010000110101101101100111111001010001101101001001111010110010111001011010000001100110101000101111000001111101111110010000010101110011110101101010110001100011101111011100010011101100111110010111111100110101000000111101000000000110100100101111101000110101010101101001110001110000101011010101100011100100111100010001011010010001100011111110010011010011000111000100111100010110100011010010101011011011111110100001110000011011\n", "output": "1110010010010000110101101101100111111001010001101101001001111010110010111001011010000001100110101000101111000001111101111110010000010101110011110101101010110001100011101111011100010011101100111110010111111100110101000000111101000000000110100100101111101000110101010101101001110001110000101011010101100011100100111100010001011010010001100011111110010011010011000111000100111100010110100011010010101011011011111110100001110000011011\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "11\n", "output": "1\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "111\n", "output": "11\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "111111\n", "output": "11111\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "11111\n", "output": "1111\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "1111\n", "output": "111\n", "metadata": {"func_name": null}}]	livecodebench	deepcoder_8	8
Solve the following coding problem using the programming language python: It is so boring in the summer holiday, isn't it? So Alice and Bob have invented a new game to play. The rules are as follows. First, they get a set of n distinct integers. And then they take turns to make the following moves. During each move, either Alice or Bob (the player whose turn is the current) can choose two distinct integers x and y from the set, such that the set doesn't contain their absolute difference \|x - y\|. Then this player adds integer \|x - y\| to the set (so, the size of the set increases by one). If the current player has no valid move, he (or she) loses the game. The question is who will finally win the game if both players play optimally. Remember that Alice always moves first. -----Input----- The first line contains an integer n (2 ≤ n ≤ 100) — the initial number of elements in the set. The second line contains n distinct space-separated integers a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ 10^9) — the elements of the set. -----Output----- Print a single line with the winner's name. If Alice wins print "Alice", otherwise print "Bob" (without quotes). -----Examples----- Input 2 2 3 Output Alice Input 2 5 3 Output Alice Input 3 5 6 7 Output Bob -----Note----- Consider the first test sample. Alice moves first, and the only move she can do is to choose 2 and 3, then to add 1 to the set. Next Bob moves, there is no valid move anymore, so the winner is Alice. The input will be stdin and you should print your solution to stdout Now solve the problem and return the code.	[ "```python\ndef gcd(a, b):\n while b > 0:\n a, b = b, a % b\n return a\n\nn = int(input())\nA = list(map(int, input().split()))\n\nGCD = A[0]\nfor x in A[1:]:\n GCD = gcd(GCD, x)\nnum = max(A) // GCD - n\nif num % 2 == 0:\n print(\"Bob\")\nelse:\n print(\"Alice\")\n\n\n```" ]	[{"type": "stdin_stdout", "input": "2\n2 3\n", "output": "Alice\n"}, {"type": "stdin_stdout", "input": "2\n5 3\n", "output": "Alice\n"}, {"type": "stdin_stdout", "input": "3\n5 6 7\n", "output": "Bob\n"}, {"type": "stdin_stdout", "input": "10\n72 96 24 66 6 18 12 30 60 48\n", "output": "Bob\n"}, {"type": "stdin_stdout", "input": "10\n78 66 6 60 18 84 36 96 72 48\n", "output": "Bob\n"}, {"type": "stdin_stdout", "input": "10\n98 63 42 56 14 77 70 35 84 21\n", "output": "Bob\n"}, {"type": "stdin_stdout", "input": "2\n1 1000000000\n", "output": "Bob\n"}, {"type": "stdin_stdout", "input": "2\n1000000000 999999999\n", "output": "Bob\n"}, {"type": "stdin_stdout", "input": "3\n2 4 6\n", "output": "Bob\n"}, {"type": "stdin_stdout", "input": "2\n4 6\n", "output": "Alice\n"}, {"type": "stdin_stdout", "input": "2\n2 6\n", "output": "Alice\n"}, {"type": "stdin_stdout", "input": "2\n6 2\n", "output": "Alice\n"}, {"type": "stdin_stdout", "input": "10\n100000000 200000000 300000000 400000000 500000000 600000000 700000000 800000000 900000000 1000000000\n", "output": "Bob\n"}, {"type": "stdin_stdout", "input": "2\n1 2\n", "output": "Bob\n"}, {"type": "stdin_stdout", "input": "10\n1 999999999 999999998 999999997 999999996 999999995 999999994 999999993 999999992 999999991\n", "output": "Alice\n"}, {"type": "stdin_stdout", "input": "3\n6 14 21\n", "output": "Bob\n"}, {"type": "stdin_stdout", "input": "3\n4 12 18\n", "output": "Bob\n"}, {"type": "stdin_stdout", "input": "4\n2 3 15 30\n", "output": "Bob\n"}, {"type": "stdin_stdout", "input": "2\n10 4\n", "output": "Alice\n"}]	null	null	You are an expert Python programmer. You will be given a question (problem specification) and will generate a correct Python program that matches the specification and passes all tests. Solve the following coding problem using the programming language python: It is so boring in the summer holiday, isn't it? So Alice and Bob have invented a new game to play. The rules are as follows. First, they get a set of n distinct integers. And then they take turns to make the following moves. During each move, either Alice or Bob (the player whose turn is the current) can choose two distinct integers x and y from the set, such that the set doesn't contain their absolute difference \|x - y\|. Then this player adds integer \|x - y\| to the set (so, the size of the set increases by one). If the current player has no valid move, he (or she) loses the game. The question is who will finally win the game if both players play optimally. Remember that Alice always moves first. -----Input----- The first line contains an integer n (2 ≤ n ≤ 100) — the initial number of elements in the set. The second line contains n distinct space-separated integers a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ 10^9) — the elements of the set. -----Output----- Print a single line with the winner's name. If Alice wins print "Alice", otherwise print "Bob" (without quotes). -----Examples----- Input 2 2 3 Output Alice Input 2 5 3 Output Alice Input 3 5 6 7 Output Bob -----Note----- Consider the first test sample. Alice moves first, and the only move she can do is to choose 2 and 3, then to add 1 to the set. Next Bob moves, there is no valid move anymore, so the winner is Alice. The input will be stdin and you should print your solution to stdout Now solve the problem and return the code.### Format: Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within delimiters as follows. Ensure that when the python program runs, it reads the inputs, runs the algorithm and writes output to STDOUT. ```python # YOUR CODE HERE ``` ### Answer: (use the provided format with backticks)	[{"type": "stdin_stdout", "input": "2\n2 3\n", "output": "Alice\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "2\n5 3\n", "output": "Alice\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "3\n5 6 7\n", "output": "Bob\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "10\n72 96 24 66 6 18 12 30 60 48\n", "output": "Bob\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "10\n78 66 6 60 18 84 36 96 72 48\n", "output": "Bob\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "10\n98 63 42 56 14 77 70 35 84 21\n", "output": "Bob\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "2\n1 1000000000\n", "output": "Bob\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "2\n1000000000 999999999\n", "output": "Bob\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "3\n2 4 6\n", "output": "Bob\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "2\n4 6\n", "output": "Alice\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "2\n2 6\n", "output": "Alice\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "2\n6 2\n", "output": "Alice\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "10\n100000000 200000000 300000000 400000000 500000000 600000000 700000000 800000000 900000000 1000000000\n", "output": "Bob\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "2\n1 2\n", "output": "Bob\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "10\n1 999999999 999999998 999999997 999999996 999999995 999999994 999999993 999999992 999999991\n", "output": "Alice\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "3\n6 14 21\n", "output": "Bob\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "3\n4 12 18\n", "output": "Bob\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "4\n2 3 15 30\n", "output": "Bob\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "2\n10 4\n", "output": "Alice\n", "metadata": {"func_name": null}}]	livecodebench	deepcoder_9	9
Solve the following coding problem using the programming language python: Mad scientist Mike does not use slow hard disks. His modification of a hard drive has not one, but n different heads that can read data in parallel. When viewed from the side, Mike's hard drive is an endless array of tracks. The tracks of the array are numbered from left to right with integers, starting with 1. In the initial state the i-th reading head is above the track number h_{i}. For each of the reading heads, the hard drive's firmware can move the head exactly one track to the right or to the left, or leave it on the current track. During the operation each head's movement does not affect the movement of the other heads: the heads can change their relative order; there can be multiple reading heads above any of the tracks. A track is considered read if at least one head has visited this track. In particular, all of the tracks numbered h_1, h_2, ..., h_{n} have been read at the beginning of the operation. [Image] Mike needs to read the data on m distinct tracks with numbers p_1, p_2, ..., p_{m}. Determine the minimum time the hard drive firmware needs to move the heads and read all the given tracks. Note that an arbitrary number of other tracks can also be read. -----Input----- The first line of the input contains two space-separated integers n, m (1 ≤ n, m ≤ 10^5) — the number of disk heads and the number of tracks to read, accordingly. The second line contains n distinct integers h_{i} in ascending order (1 ≤ h_{i} ≤ 10^10, h_{i} < h_{i} + 1) — the initial positions of the heads. The third line contains m distinct integers p_{i} in ascending order (1 ≤ p_{i} ≤ 10^10, p_{i} < p_{i} + 1) - the numbers of tracks to read. Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is recommended to use the cin, cout streams or the %I64d specifier. -----Output----- Print a single number — the minimum time required, in seconds, to read all the needed tracks. -----Examples----- Input 3 4 2 5 6 1 3 6 8 Output 2 Input 3 3 1 2 3 1 2 3 Output 0 Input 1 2 165 142 200 Output 81 -----Note----- The first test coincides with the figure. In this case the given tracks can be read in 2 seconds in the following way: during the first second move the 1-st head to the left and let it stay there; move the second head to the left twice; move the third head to the right twice (note that the 6-th track has already been read at the beginning). One cannot read the tracks in 1 second as the 3-rd head is at distance 2 from the 8-th track. The input will be stdin and you should print your solution to stdout Now solve the problem and return the code.	[ "```python\nimport sys\nfrom itertools import \nfrom math import \ndef solve():\n n, m = map(int, input().split())\n h = list(map(int, input().split()))\n p = list(map(int, input().split()))\n ss, ll = 0, int(2.2e10)\n while ss < ll:\n avg = (ss + ll) // 2\n works = True\n hidx = 0\n pidx = 0\n while hidx < len(h) and pidx < len(p):\n leftget = p[pidx]\n curpos = h[hidx]\n if curpos - leftget > avg:\n works = False\n break\n getbacktime = max(0, 2*(curpos - leftget))\n alsotoright = max(0, avg - getbacktime)\n leftime = max(0, curpos - leftget)\n remtime = max(0, (avg - leftime) // 2)\n furthestright = curpos + max(alsotoright, remtime)\n while pidx < len(p) and p[pidx] <= furthestright: pidx += 1\n hidx += 1\n if pidx != len(p): works = False\n if works: ll = avg\n else: ss = avg + 1\n print(ss)\n\n\nif sys.hexversion == 50594544 : sys.stdin = open(\"test.txt\")\nsolve()\n```" ]	[{"type": "stdin_stdout", "input": "3 4\n2 5 6\n1 3 6 8\n", "output": "2\n"}, {"type": "stdin_stdout", "input": "3 3\n1 2 3\n1 2 3\n", "output": "0\n"}, {"type": "stdin_stdout", "input": "1 2\n165\n142 200\n", "output": "81\n"}, {"type": "stdin_stdout", "input": "1 2\n5000000000\n1 10000000000\n", "output": "14999999998\n"}, {"type": "stdin_stdout", "input": "2 4\n3 12\n1 7 8 14\n", "output": "8\n"}, {"type": "stdin_stdout", "input": "3 3\n1 2 3\n2 3 4\n", "output": "1\n"}, {"type": "stdin_stdout", "input": "2 1\n1 10\n9\n", "output": "1\n"}, {"type": "stdin_stdout", "input": "3 19\n7 10 13\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19\n", "output": "6\n"}, {"type": "stdin_stdout", "input": "3 3\n2 3 4\n1 3 5\n", "output": "1\n"}, {"type": "stdin_stdout", "input": "10 11\n1 909090909 1818181817 2727272725 3636363633 4545454541 5454545449 6363636357 7272727265 8181818173\n454545455 1363636363 2272727271 3181818179 4090909087 4999999995 5909090903 6818181811 7727272719 8636363627 9545454535\n", "output": "1363636362\n"}, {"type": "stdin_stdout", "input": "3 10\n4999999999 5000000000 5000000001\n1 1000 100000 1000000 4999999999 5000000000 5000000001 6000000000 8000000000 10000000000\n", "output": "4999999999\n"}, {"type": "stdin_stdout", "input": "2 4\n4500000000 5500000000\n5 499999999 5000000001 9999999995\n", "output": "5499999993\n"}, {"type": "stdin_stdout", "input": "10 10\n331462447 1369967506 1504296131 2061390288 2309640071 3006707770 4530801731 4544099460 7357049371 9704808257\n754193799 3820869903 4594383880 5685752675 6303322854 6384906441 7863448848 8542634752 9573124462 9665646063\n", "output": "1840806981\n"}, {"type": "stdin_stdout", "input": "1 1\n10000000000\n1\n", "output": "9999999999\n"}, {"type": "stdin_stdout", "input": "1 1\n1\n10000000000\n", "output": "9999999999\n"}, {"type": "stdin_stdout", "input": "10 10\n9999999991 9999999992 9999999993 9999999994 9999999995 9999999996 9999999997 9999999998 9999999999 10000000000\n1 2 3 4 5 6 7 8 9 10\n", "output": "9999999990\n"}, {"type": "stdin_stdout", "input": "3 12\n477702277 4717363935 8947981095\n477702276 477702304 477702312 477702317 4717363895 4717363896 4717363920 4717363936 8947981094 8947981111 8947981112 8947981135\n", "output": "42\n"}, {"type": "stdin_stdout", "input": "10 10\n389151626 1885767612 2609703695 3054567325 4421751790 5636236054 6336088034 7961001379 8631992167 9836923433\n389144165 389158510 1885760728 1885775073 2609696234 2609710579 3054559864 3054574209 4421744329 4421758674\n", "output": "21229\n"}, {"type": "stdin_stdout", "input": "1 1\n10000000000\n1\n", "output": "9999999999\n"}]	null	null	You are an expert Python programmer. You will be given a question (problem specification) and will generate a correct Python program that matches the specification and passes all tests. Solve the following coding problem using the programming language python: Mad scientist Mike does not use slow hard disks. His modification of a hard drive has not one, but n different heads that can read data in parallel. When viewed from the side, Mike's hard drive is an endless array of tracks. The tracks of the array are numbered from left to right with integers, starting with 1. In the initial state the i-th reading head is above the track number h_{i}. For each of the reading heads, the hard drive's firmware can move the head exactly one track to the right or to the left, or leave it on the current track. During the operation each head's movement does not affect the movement of the other heads: the heads can change their relative order; there can be multiple reading heads above any of the tracks. A track is considered read if at least one head has visited this track. In particular, all of the tracks numbered h_1, h_2, ..., h_{n} have been read at the beginning of the operation. [Image] Mike needs to read the data on m distinct tracks with numbers p_1, p_2, ..., p_{m}. Determine the minimum time the hard drive firmware needs to move the heads and read all the given tracks. Note that an arbitrary number of other tracks can also be read. -----Input----- The first line of the input contains two space-separated integers n, m (1 ≤ n, m ≤ 10^5) — the number of disk heads and the number of tracks to read, accordingly. The second line contains n distinct integers h_{i} in ascending order (1 ≤ h_{i} ≤ 10^10, h_{i} < h_{i} + 1) — the initial positions of the heads. The third line contains m distinct integers p_{i} in ascending order (1 ≤ p_{i} ≤ 10^10, p_{i} < p_{i} + 1) - the numbers of tracks to read. Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is recommended to use the cin, cout streams or the %I64d specifier. -----Output----- Print a single number — the minimum time required, in seconds, to read all the needed tracks. -----Examples----- Input 3 4 2 5 6 1 3 6 8 Output 2 Input 3 3 1 2 3 1 2 3 Output 0 Input 1 2 165 142 200 Output 81 -----Note----- The first test coincides with the figure. In this case the given tracks can be read in 2 seconds in the following way: during the first second move the 1-st head to the left and let it stay there; move the second head to the left twice; move the third head to the right twice (note that the 6-th track has already been read at the beginning). One cannot read the tracks in 1 second as the 3-rd head is at distance 2 from the 8-th track. The input will be stdin and you should print your solution to stdout Now solve the problem and return the code.### Format: Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within delimiters as follows. Ensure that when the python program runs, it reads the inputs, runs the algorithm and writes output to STDOUT. ```python # YOUR CODE HERE ``` ### Answer: (use the provided format with backticks)	[{"type": "stdin_stdout", "input": "3 4\n2 5 6\n1 3 6 8\n", "output": "2\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "3 3\n1 2 3\n1 2 3\n", "output": "0\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "1 2\n165\n142 200\n", "output": "81\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "1 2\n5000000000\n1 10000000000\n", "output": "14999999998\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "2 4\n3 12\n1 7 8 14\n", "output": "8\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "3 3\n1 2 3\n2 3 4\n", "output": "1\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "2 1\n1 10\n9\n", "output": "1\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "3 19\n7 10 13\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19\n", "output": "6\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "3 3\n2 3 4\n1 3 5\n", "output": "1\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "10 11\n1 909090909 1818181817 2727272725 3636363633 4545454541 5454545449 6363636357 7272727265 8181818173\n454545455 1363636363 2272727271 3181818179 4090909087 4999999995 5909090903 6818181811 7727272719 8636363627 9545454535\n", "output": "1363636362\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "3 10\n4999999999 5000000000 5000000001\n1 1000 100000 1000000 4999999999 5000000000 5000000001 6000000000 8000000000 10000000000\n", "output": "4999999999\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "2 4\n4500000000 5500000000\n5 499999999 5000000001 9999999995\n", "output": "5499999993\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "10 10\n331462447 1369967506 1504296131 2061390288 2309640071 3006707770 4530801731 4544099460 7357049371 9704808257\n754193799 3820869903 4594383880 5685752675 6303322854 6384906441 7863448848 8542634752 9573124462 9665646063\n", "output": "1840806981\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "1 1\n10000000000\n1\n", "output": "9999999999\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "1 1\n1\n10000000000\n", "output": "9999999999\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "10 10\n9999999991 9999999992 9999999993 9999999994 9999999995 9999999996 9999999997 9999999998 9999999999 10000000000\n1 2 3 4 5 6 7 8 9 10\n", "output": "9999999990\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "3 12\n477702277 4717363935 8947981095\n477702276 477702304 477702312 477702317 4717363895 4717363896 4717363920 4717363936 8947981094 8947981111 8947981112 8947981135\n", "output": "42\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "10 10\n389151626 1885767612 2609703695 3054567325 4421751790 5636236054 6336088034 7961001379 8631992167 9836923433\n389144165 389158510 1885760728 1885775073 2609696234 2609710579 3054559864 3054574209 4421744329 4421758674\n", "output": "21229\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "1 1\n10000000000\n1\n", "output": "9999999999\n", "metadata": {"func_name": null}}]	livecodebench	deepcoder_10	10
Solve the following coding problem using the programming language python: A schoolboy named Vasya loves reading books on programming and mathematics. He has recently read an encyclopedia article that described the method of median smoothing (or median filter) and its many applications in science and engineering. Vasya liked the idea of the method very much, and he decided to try it in practice. Applying the simplest variant of median smoothing to the sequence of numbers a_1, a_2, ..., a_{n} will result a new sequence b_1, b_2, ..., b_{n} obtained by the following algorithm: b_1 = a_1, b_{n} = a_{n}, that is, the first and the last number of the new sequence match the corresponding numbers of the original sequence. For i = 2, ..., n - 1 value b_{i} is equal to the median of three values a_{i} - 1, a_{i} and a_{i} + 1. The median of a set of three numbers is the number that goes on the second place, when these three numbers are written in the non-decreasing order. For example, the median of the set 5, 1, 2 is number 2, and the median of set 1, 0, 1 is equal to 1. In order to make the task easier, Vasya decided to apply the method to sequences consisting of zeros and ones only. Having made the procedure once, Vasya looked at the resulting sequence and thought: what if I apply the algorithm to it once again, and then apply it to the next result, and so on? Vasya tried a couple of examples and found out that after some number of median smoothing algorithm applications the sequence can stop changing. We say that the sequence is stable, if it does not change when the median smoothing is applied to it. Now Vasya wonders, whether the sequence always eventually becomes stable. He asks you to write a program that, given a sequence of zeros and ones, will determine whether it ever becomes stable. Moreover, if it ever becomes stable, then you should determine what will it look like and how many times one needs to apply the median smoothing algorithm to initial sequence in order to obtain a stable one. -----Input----- The first input line of the input contains a single integer n (3 ≤ n ≤ 500 000) — the length of the initial sequence. The next line contains n integers a_1, a_2, ..., a_{n} (a_{i} = 0 or a_{i} = 1), giving the initial sequence itself. -----Output----- If the sequence will never become stable, print a single number - 1. Otherwise, first print a single integer — the minimum number of times one needs to apply the median smoothing algorithm to the initial sequence before it becomes is stable. In the second line print n numbers separated by a space — the resulting sequence itself. -----Examples----- Input 4 0 0 1 1 Output 0 0 0 1 1 Input 5 0 1 0 1 0 Output 2 0 0 0 0 0 -----Note----- In the second sample the stabilization occurs in two steps: $01010 \rightarrow 00100 \rightarrow 00000$, and the sequence 00000 is obviously stable. The input will be stdin and you should print your solution to stdout Now solve the problem and return the code.	[ "```python\nfrom sys import stdin\n\n#stdin = open('input.txt')\n\nn = int(stdin.readline())\n\nseq = [int(x) for x in stdin.readline().split()]\ncarry = seq[0]\nresult = [carry]\n\nmark = False\ncur_len = 0\nmax_len = 0\n\ni = 1\nwhile i < len(seq) - 1:\n if mark:\n if seq[i] != seq[i + 1]:\n cur_len += 1\n else:\n if cur_len > max_len:\n max_len = cur_len\n\n if seq[i] == carry:\n result.extend([carry]cur_len)\n else:\n result.extend([carry](cur_len//2))\n result.extend([seq[i]](cur_len//2))\n\n result.append(seq[i])\n mark = False\n cur_len = 0\n elif seq[i] != seq[i - 1] and seq[i] != seq[i + 1]:\n mark = True\n cur_len = 1\n carry = seq[i - 1]\n else:\n result.append(seq[i])\n\n i += 1\n\nif mark:\n if cur_len > max_len:\n max_len = cur_len\n\n if seq[i] == carry:\n result.extend([carry]cur_len)\n else:\n result.extend([carry](cur_len//2))\n result.extend([seq[i]](cur_len//2))\n\nresult.append(seq[i])\n\nprint((max_len + 1)//2)\nfor x in result:\n print(x, end=' ')\n```" ]	[{"type": "stdin_stdout", "input": "4\n0 0 1 1\n", "output": "0\n0 0 1 1\n"}, {"type": "stdin_stdout", "input": "5\n0 1 0 1 0\n", "output": "2\n0 0 0 0 0\n"}, {"type": "stdin_stdout", "input": "3\n1 0 0\n", "output": "0\n1 0 0\n"}, {"type": "stdin_stdout", "input": "4\n1 0 0 1\n", "output": "0\n1 0 0 1\n"}, {"type": "stdin_stdout", "input": "7\n1 0 1 1 1 0 1\n", "output": "1\n1 1 1 1 1 1 1\n"}, {"type": "stdin_stdout", "input": "14\n0 1 0 0 0 1 1 0 1 0 1 0 1 0\n", "output": "3\n0 0 0 0 0 1 1 1 1 1 0 0 0 0\n"}, {"type": "stdin_stdout", "input": "3\n1 0 1\n", "output": "1\n1 1 1\n"}, {"type": "stdin_stdout", "input": "3\n0 0 1\n", "output": "0\n0 0 1\n"}, {"type": "stdin_stdout", "input": "3\n1 1 0\n", "output": "0\n1 1 0\n"}, {"type": "stdin_stdout", "input": "3\n1 1 1\n", "output": "0\n1 1 1\n"}, {"type": "stdin_stdout", "input": "4\n1 1 0 1\n", "output": "1\n1 1 1 1\n"}, {"type": "stdin_stdout", "input": "4\n1 0 1 1\n", "output": "1\n1 1 1 1\n"}, {"type": "stdin_stdout", "input": "10\n0 1 0 1 0 0 1 0 1 0\n", "output": "2\n0 0 0 0 0 0 0 0 0 0\n"}, {"type": "stdin_stdout", "input": "4\n0 1 1 0\n", "output": "0\n0 1 1 0\n"}, {"type": "stdin_stdout", "input": "168\n0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 1 0 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 0 1 0 1 0 1 0 1 0\n", "output": "36\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n"}, {"type": "stdin_stdout", "input": "3\n0 1 1\n", "output": "0\n0 1 1\n"}, {"type": "stdin_stdout", "input": "3\n0 0 0\n", "output": "0\n0 0 0\n"}, {"type": "stdin_stdout", "input": "4\n0 1 0 1\n", "output": "1\n0 0 1 1\n"}, {"type": "stdin_stdout", "input": "3\n0 1 0\n", "output": "1\n0 0 0\n"}]	null	null	You are an expert Python programmer. You will be given a question (problem specification) and will generate a correct Python program that matches the specification and passes all tests. Solve the following coding problem using the programming language python: A schoolboy named Vasya loves reading books on programming and mathematics. He has recently read an encyclopedia article that described the method of median smoothing (or median filter) and its many applications in science and engineering. Vasya liked the idea of the method very much, and he decided to try it in practice. Applying the simplest variant of median smoothing to the sequence of numbers a_1, a_2, ..., a_{n} will result a new sequence b_1, b_2, ..., b_{n} obtained by the following algorithm: b_1 = a_1, b_{n} = a_{n}, that is, the first and the last number of the new sequence match the corresponding numbers of the original sequence. For i = 2, ..., n - 1 value b_{i} is equal to the median of three values a_{i} - 1, a_{i} and a_{i} + 1. The median of a set of three numbers is the number that goes on the second place, when these three numbers are written in the non-decreasing order. For example, the median of the set 5, 1, 2 is number 2, and the median of set 1, 0, 1 is equal to 1. In order to make the task easier, Vasya decided to apply the method to sequences consisting of zeros and ones only. Having made the procedure once, Vasya looked at the resulting sequence and thought: what if I apply the algorithm to it once again, and then apply it to the next result, and so on? Vasya tried a couple of examples and found out that after some number of median smoothing algorithm applications the sequence can stop changing. We say that the sequence is stable, if it does not change when the median smoothing is applied to it. Now Vasya wonders, whether the sequence always eventually becomes stable. He asks you to write a program that, given a sequence of zeros and ones, will determine whether it ever becomes stable. Moreover, if it ever becomes stable, then you should determine what will it look like and how many times one needs to apply the median smoothing algorithm to initial sequence in order to obtain a stable one. -----Input----- The first input line of the input contains a single integer n (3 ≤ n ≤ 500 000) — the length of the initial sequence. The next line contains n integers a_1, a_2, ..., a_{n} (a_{i} = 0 or a_{i} = 1), giving the initial sequence itself. -----Output----- If the sequence will never become stable, print a single number - 1. Otherwise, first print a single integer — the minimum number of times one needs to apply the median smoothing algorithm to the initial sequence before it becomes is stable. In the second line print n numbers separated by a space — the resulting sequence itself. -----Examples----- Input 4 0 0 1 1 Output 0 0 0 1 1 Input 5 0 1 0 1 0 Output 2 0 0 0 0 0 -----Note----- In the second sample the stabilization occurs in two steps: $01010 \rightarrow 00100 \rightarrow 00000$, and the sequence 00000 is obviously stable. The input will be stdin and you should print your solution to stdout Now solve the problem and return the code.### Format: Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within delimiters as follows. Ensure that when the python program runs, it reads the inputs, runs the algorithm and writes output to STDOUT. ```python # YOUR CODE HERE ``` ### Answer: (use the provided format with backticks)	[{"type": "stdin_stdout", "input": "4\n0 0 1 1\n", "output": "0\n0 0 1 1\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "5\n0 1 0 1 0\n", "output": "2\n0 0 0 0 0\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "3\n1 0 0\n", "output": "0\n1 0 0\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "4\n1 0 0 1\n", "output": "0\n1 0 0 1\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "7\n1 0 1 1 1 0 1\n", "output": "1\n1 1 1 1 1 1 1\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "14\n0 1 0 0 0 1 1 0 1 0 1 0 1 0\n", "output": "3\n0 0 0 0 0 1 1 1 1 1 0 0 0 0\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "3\n1 0 1\n", "output": "1\n1 1 1\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "3\n0 0 1\n", "output": "0\n0 0 1\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "3\n1 1 0\n", "output": "0\n1 1 0\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "3\n1 1 1\n", "output": "0\n1 1 1\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "4\n1 1 0 1\n", "output": "1\n1 1 1 1\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "4\n1 0 1 1\n", "output": "1\n1 1 1 1\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "10\n0 1 0 1 0 0 1 0 1 0\n", "output": "2\n0 0 0 0 0 0 0 0 0 0\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "4\n0 1 1 0\n", "output": "0\n0 1 1 0\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "168\n0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 1 0 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 0 1 0 1 0 1 0 1 0\n", "output": "36\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "3\n0 1 1\n", "output": "0\n0 1 1\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "3\n0 0 0\n", "output": "0\n0 0 0\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "4\n0 1 0 1\n", "output": "1\n0 0 1 1\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "3\n0 1 0\n", "output": "1\n0 0 0\n", "metadata": {"func_name": null}}]	livecodebench	deepcoder_11	11
Solve the following coding problem using the programming language python: For a vector $\vec{v} = (x, y)$, define $\|v\| = \sqrt{x^2 + y^2}$. Allen had a bit too much to drink at the bar, which is at the origin. There are $n$ vectors $\vec{v_1}, \vec{v_2}, \cdots, \vec{v_n}$. Allen will make $n$ moves. As Allen's sense of direction is impaired, during the $i$-th move he will either move in the direction $\vec{v_i}$ or $-\vec{v_i}$. In other words, if his position is currently $p = (x, y)$, he will either move to $p + \vec{v_i}$ or $p - \vec{v_i}$. Allen doesn't want to wander too far from home (which happens to also be the bar). You need to help him figure out a sequence of moves (a sequence of signs for the vectors) such that his final position $p$ satisfies $\|p\| \le 1.5 \cdot 10^6$ so that he can stay safe. -----Input----- The first line contains a single integer $n$ ($1 \le n \le 10^5$) — the number of moves. Each of the following lines contains two space-separated integers $x_i$ and $y_i$, meaning that $\vec{v_i} = (x_i, y_i)$. We have that $\|v_i\| \le 10^6$ for all $i$. -----Output----- Output a single line containing $n$ integers $c_1, c_2, \cdots, c_n$, each of which is either $1$ or $-1$. Your solution is correct if the value of $p = \sum_{i = 1}^n c_i \vec{v_i}$, satisfies $\|p\| \le 1.5 \cdot 10^6$. It can be shown that a solution always exists under the given constraints. -----Examples----- Input 3 999999 0 0 999999 999999 0 Output 1 1 -1 Input 1 -824590 246031 Output 1 Input 8 -67761 603277 640586 -396671 46147 -122580 569609 -2112 400 914208 131792 309779 -850150 -486293 5272 721899 Output 1 1 1 1 1 1 1 -1 The input will be stdin and you should print your solution to stdout Now solve the problem and return the code.	[ "```python\nimport random\n\nn = int(input())\nv = []\na = []\nfor i in range(n):\n a.append(i)\n\nfor _ in range(0, n):\n x, y = list(map(int, input().split()))\n v.append([x, y, xx+yy])\n\nwhile 1>0:\n x = 0\n y = 0\n ans = [0]n\n random.shuffle(a)\n for i in range(n):\n if (x+v[a[i]][0])2+(y+v[a[i]][1])2 <= (x-v[a[i]][0])2+(y-v[a[i]][1])2:\n x += v[a[i]][0]\n y += v[a[i]][1]\n ans[a[i]] = 1\n else:\n x -= v[a[i]][0]\n y -= v[a[i]][1]\n ans[a[i]] = -1\n if xx+yy <= 15000002:\n print(ans)\n break\n\n\n```" ]	[{"type": "stdin_stdout", "input": "3\n999999 0\n0 999999\n999999 0\n", "output": "1 1 -1 \n"}, {"type": "stdin_stdout", "input": "1\n-824590 246031\n", "output": "1 \n"}, {"type": "stdin_stdout", "input": "8\n-67761 603277\n640586 -396671\n46147 -122580\n569609 -2112\n400 914208\n131792 309779\n-850150 -486293\n5272 721899\n", "output": "1 1 1 1 1 1 1 -1 \n"}, {"type": "stdin_stdout", "input": "6\n1000000 0\n1000000 0\n-1000000 0\n0 1000000\n0 -1000000\n0 -1000000\n", "output": "1 1 1 1 1 1 \n"}, {"type": "stdin_stdout", "input": "8\n-411248 143802\n300365 629658\n363219 343742\n396148 -94037\n-722124 467785\n-178147 -931253\n265458 73307\n-621502 -709713\n", "output": "1 1 1 1 1 1 1 -1 \n"}, {"type": "stdin_stdout", "input": "3\n1000000 0\n0 999999\n600000 -600000\n", "output": "-1 1 1 \n"}, {"type": "stdin_stdout", "input": "5\n140239 46311\n399464 -289055\n-540174 823360\n538102 -373313\n326189 933934\n", "output": "1 1 1 1 -1 \n"}, {"type": "stdin_stdout", "input": "3\n1000000 0\n0 999999\n300000 -300000\n", "output": "1 1 -1 \n"}, {"type": "stdin_stdout", "input": "9\n1000000 0\n0 -999999\n600000 600000\n600000 600000\n600000 600000\n-600000 -600000\n600000 600000\n600000 600000\n-700000 710000\n", "output": "1 1 1 -1 1 1 1 -1 1 \n"}, {"type": "stdin_stdout", "input": "2\n1 999999\n1 -999999\n", "output": "1 1 \n"}, {"type": "stdin_stdout", "input": "2\n999999 1\n999999 -1\n", "output": "1 -1 \n"}, {"type": "stdin_stdout", "input": "2\n-1 999999\n-1 -999999\n", "output": "1 1 \n"}, {"type": "stdin_stdout", "input": "2\n-999999 -1\n-999999 1\n", "output": "1 -1 \n"}, {"type": "stdin_stdout", "input": "2\n999999 1\n-999999 1\n", "output": "1 1 \n"}, {"type": "stdin_stdout", "input": "2\n999999 -1\n-999999 -1\n", "output": "1 1 \n"}, {"type": "stdin_stdout", "input": "2\n1 999999\n-1 999999\n", "output": "1 -1 \n"}, {"type": "stdin_stdout", "input": "2\n1 -999999\n-1 -999999\n", "output": "1 -1 \n"}, {"type": "stdin_stdout", "input": "4\n1000000 0\n-1 999999\n600000 -600000\n0 0\n", "output": "-1 1 1 1 \n"}, {"type": "stdin_stdout", "input": "2\n999999 -1\n-1 999999\n", "output": "1 1 \n"}]	null	null	You are an expert Python programmer. You will be given a question (problem specification) and will generate a correct Python program that matches the specification and passes all tests. Solve the following coding problem using the programming language python: For a vector $\vec{v} = (x, y)$, define $\|v\| = \sqrt{x^2 + y^2}$. Allen had a bit too much to drink at the bar, which is at the origin. There are $n$ vectors $\vec{v_1}, \vec{v_2}, \cdots, \vec{v_n}$. Allen will make $n$ moves. As Allen's sense of direction is impaired, during the $i$-th move he will either move in the direction $\vec{v_i}$ or $-\vec{v_i}$. In other words, if his position is currently $p = (x, y)$, he will either move to $p + \vec{v_i}$ or $p - \vec{v_i}$. Allen doesn't want to wander too far from home (which happens to also be the bar). You need to help him figure out a sequence of moves (a sequence of signs for the vectors) such that his final position $p$ satisfies $\|p\| \le 1.5 \cdot 10^6$ so that he can stay safe. -----Input----- The first line contains a single integer $n$ ($1 \le n \le 10^5$) — the number of moves. Each of the following lines contains two space-separated integers $x_i$ and $y_i$, meaning that $\vec{v_i} = (x_i, y_i)$. We have that $\|v_i\| \le 10^6$ for all $i$. -----Output----- Output a single line containing $n$ integers $c_1, c_2, \cdots, c_n$, each of which is either $1$ or $-1$. Your solution is correct if the value of $p = \sum_{i = 1}^n c_i \vec{v_i}$, satisfies $\|p\| \le 1.5 \cdot 10^6$. It can be shown that a solution always exists under the given constraints. -----Examples----- Input 3 999999 0 0 999999 999999 0 Output 1 1 -1 Input 1 -824590 246031 Output 1 Input 8 -67761 603277 640586 -396671 46147 -122580 569609 -2112 400 914208 131792 309779 -850150 -486293 5272 721899 Output 1 1 1 1 1 1 1 -1 The input will be stdin and you should print your solution to stdout Now solve the problem and return the code.### Format: Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within delimiters as follows. Ensure that when the python program runs, it reads the inputs, runs the algorithm and writes output to STDOUT. ```python # YOUR CODE HERE ``` ### Answer: (use the provided format with backticks)	[{"type": "stdin_stdout", "input": "3\n999999 0\n0 999999\n999999 0\n", "output": "1 1 -1 \n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "1\n-824590 246031\n", "output": "1 \n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "8\n-67761 603277\n640586 -396671\n46147 -122580\n569609 -2112\n400 914208\n131792 309779\n-850150 -486293\n5272 721899\n", "output": "1 1 1 1 1 1 1 -1 \n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "6\n1000000 0\n1000000 0\n-1000000 0\n0 1000000\n0 -1000000\n0 -1000000\n", "output": "1 1 1 1 1 1 \n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "8\n-411248 143802\n300365 629658\n363219 343742\n396148 -94037\n-722124 467785\n-178147 -931253\n265458 73307\n-621502 -709713\n", "output": "1 1 1 1 1 1 1 -1 \n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "3\n1000000 0\n0 999999\n600000 -600000\n", "output": "-1 1 1 \n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "5\n140239 46311\n399464 -289055\n-540174 823360\n538102 -373313\n326189 933934\n", "output": "1 1 1 1 -1 \n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "3\n1000000 0\n0 999999\n300000 -300000\n", "output": "1 1 -1 \n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "9\n1000000 0\n0 -999999\n600000 600000\n600000 600000\n600000 600000\n-600000 -600000\n600000 600000\n600000 600000\n-700000 710000\n", "output": "1 1 1 -1 1 1 1 -1 1 \n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "2\n1 999999\n1 -999999\n", "output": "1 1 \n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "2\n999999 1\n999999 -1\n", "output": "1 -1 \n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "2\n-1 999999\n-1 -999999\n", "output": "1 1 \n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "2\n-999999 -1\n-999999 1\n", "output": "1 -1 \n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "2\n999999 1\n-999999 1\n", "output": "1 1 \n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "2\n999999 -1\n-999999 -1\n", "output": "1 1 \n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "2\n1 999999\n-1 999999\n", "output": "1 -1 \n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "2\n1 -999999\n-1 -999999\n", "output": "1 -1 \n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "4\n1000000 0\n-1 999999\n600000 -600000\n0 0\n", "output": "-1 1 1 1 \n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "2\n999999 -1\n-1 999999\n", "output": "1 1 \n", "metadata": {"func_name": null}}]	livecodebench	deepcoder_12	12
Solve the following coding problem using the programming language python: Limak is a little bear who loves to play. Today he is playing by destroying block towers. He built n towers in a row. The i-th tower is made of h_{i} identical blocks. For clarification see picture for the first sample. Limak will repeat the following operation till everything is destroyed. Block is called internal if it has all four neighbors, i.e. it has each side (top, left, down and right) adjacent to other block or to the floor. Otherwise, block is boundary. In one operation Limak destroys all boundary blocks. His paws are very fast and he destroys all those blocks at the same time. Limak is ready to start. You task is to count how many operations will it take him to destroy all towers. -----Input----- The first line contains single integer n (1 ≤ n ≤ 10^5). The second line contains n space-separated integers h_1, h_2, ..., h_{n} (1 ≤ h_{i} ≤ 10^9) — sizes of towers. -----Output----- Print the number of operations needed to destroy all towers. -----Examples----- Input 6 2 1 4 6 2 2 Output 3 Input 7 3 3 3 1 3 3 3 Output 2 -----Note----- The picture below shows all three operations for the first sample test. Each time boundary blocks are marked with red color. [Image] After first operation there are four blocks left and only one remains after second operation. This last block is destroyed in third operation. The input will be stdin and you should print your solution to stdout Now solve the problem and return the code.	[ "```python\n\nx = int(input())\ny = list(map(int, input().split(' ')))\n\ny[0] = 1\ny[x-1] = 1\n\nz = y[:]\nfor i in range(1, x):\n z[i] = min(z[i], z[i-1] + 1)\n\nw = y[:]\nfor i in range(x-2, -1, -1):\n w[i] = min(w[i], w[i+1]+1)\n\nans = 0\nfor i in range(x):\n ans = max(ans, min(z[i], w[i]))\n\nprint(ans)\n\n```" ]	[{"type": "stdin_stdout", "input": "6\n2 1 4 6 2 2\n", "output": "3\n"}, {"type": "stdin_stdout", "input": "7\n3 3 3 1 3 3 3\n", "output": "2\n"}, {"type": "stdin_stdout", "input": "7\n5128 5672 5805 5452 5882 5567 5032\n", "output": "4\n"}, {"type": "stdin_stdout", "input": "10\n1 2 2 3 5 5 5 4 2 1\n", "output": "5\n"}, {"type": "stdin_stdout", "input": "14\n20 20 20 20 20 20 3 20 20 20 20 20 20 20\n", "output": "5\n"}, {"type": "stdin_stdout", "input": "50\n3 2 4 3 5 3 4 5 3 2 3 3 3 4 5 4 2 2 3 3 4 4 3 2 3 3 2 3 4 4 5 2 5 2 3 5 4 4 2 2 3 5 2 5 2 2 5 4 5 4\n", "output": "4\n"}, {"type": "stdin_stdout", "input": "1\n1\n", "output": "1\n"}, {"type": "stdin_stdout", "input": "1\n1000000000\n", "output": "1\n"}, {"type": "stdin_stdout", "input": "2\n1 1\n", "output": "1\n"}, {"type": "stdin_stdout", "input": "2\n1049 1098\n", "output": "1\n"}, {"type": "stdin_stdout", "input": "2\n100 100\n", "output": "1\n"}, {"type": "stdin_stdout", "input": "5\n1 2 3 2 1\n", "output": "3\n"}, {"type": "stdin_stdout", "input": "15\n2 2 1 1 2 2 2 2 2 2 2 2 2 1 2\n", "output": "2\n"}, {"type": "stdin_stdout", "input": "28\n415546599 415546599 415546599 415546599 415546599 415546599 415546599 415546599 415546599 2 802811737 802811737 802811737 802811737 802811737 802811737 802811737 802811737 1 550595901 550595901 550595901 550595901 550595901 550595901 550595901 550595901 550595901\n", "output": "6\n"}, {"type": "stdin_stdout", "input": "45\n3 12 13 11 13 13 10 11 14 15 15 13 14 12 13 11 14 10 10 14 14 11 10 12 11 11 13 14 10 11 14 13 14 11 11 11 12 15 1 10 15 12 14 14 14\n", "output": "13\n"}, {"type": "stdin_stdout", "input": "84\n1 3 4 5 6 5 6 7 8 9 7 4 5 4 2 5 1 1 1 3 2 7 7 8 10 9 5 6 5 2 3 3 3 3 3 2 4 8 6 5 8 9 8 7 9 3 4 4 4 2 2 1 6 4 9 5 9 9 10 7 10 4 5 4 2 4 3 3 4 4 6 6 6 9 10 12 7 5 9 8 5 3 3 2\n", "output": "8\n"}, {"type": "stdin_stdout", "input": "170\n1 2 1 2 1 1 1 1 2 3 2 1 1 2 2 1 2 1 2 1 1 2 3 3 2 1 1 1 1 1 1 1 1 2 1 2 3 3 2 1 2 2 1 2 3 2 1 1 2 3 2 1 2 1 1 1 2 3 3 2 1 2 1 2 1 1 1 2 1 2 1 1 2 2 1 1 2 1 2 2 1 2 1 2 2 1 2 1 2 3 2 1 1 2 3 4 4 3 2 1 2 1 2 1 2 3 3 2 1 2 1 1 1 1 1 1 1 2 2 1 1 2 1 1 1 1 2 1 1 2 3 2 1 2 2 1 2 1 1 1 2 2 1 2 1 2 3 2 1 2 1 1 1 2 3 4 5 4 3 2 1 1 2 1 2 3 4 3 2 1\n", "output": "5\n"}, {"type": "stdin_stdout", "input": "1\n5\n", "output": "1\n"}]	null	null	You are an expert Python programmer. You will be given a question (problem specification) and will generate a correct Python program that matches the specification and passes all tests. Solve the following coding problem using the programming language python: Limak is a little bear who loves to play. Today he is playing by destroying block towers. He built n towers in a row. The i-th tower is made of h_{i} identical blocks. For clarification see picture for the first sample. Limak will repeat the following operation till everything is destroyed. Block is called internal if it has all four neighbors, i.e. it has each side (top, left, down and right) adjacent to other block or to the floor. Otherwise, block is boundary. In one operation Limak destroys all boundary blocks. His paws are very fast and he destroys all those blocks at the same time. Limak is ready to start. You task is to count how many operations will it take him to destroy all towers. -----Input----- The first line contains single integer n (1 ≤ n ≤ 10^5). The second line contains n space-separated integers h_1, h_2, ..., h_{n} (1 ≤ h_{i} ≤ 10^9) — sizes of towers. -----Output----- Print the number of operations needed to destroy all towers. -----Examples----- Input 6 2 1 4 6 2 2 Output 3 Input 7 3 3 3 1 3 3 3 Output 2 -----Note----- The picture below shows all three operations for the first sample test. Each time boundary blocks are marked with red color. [Image] After first operation there are four blocks left and only one remains after second operation. This last block is destroyed in third operation. The input will be stdin and you should print your solution to stdout Now solve the problem and return the code.### Format: Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within delimiters as follows. Ensure that when the python program runs, it reads the inputs, runs the algorithm and writes output to STDOUT. ```python # YOUR CODE HERE ``` ### Answer: (use the provided format with backticks)	[{"type": "stdin_stdout", "input": "6\n2 1 4 6 2 2\n", "output": "3\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "7\n3 3 3 1 3 3 3\n", "output": "2\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "7\n5128 5672 5805 5452 5882 5567 5032\n", "output": "4\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "10\n1 2 2 3 5 5 5 4 2 1\n", "output": "5\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "14\n20 20 20 20 20 20 3 20 20 20 20 20 20 20\n", "output": "5\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "50\n3 2 4 3 5 3 4 5 3 2 3 3 3 4 5 4 2 2 3 3 4 4 3 2 3 3 2 3 4 4 5 2 5 2 3 5 4 4 2 2 3 5 2 5 2 2 5 4 5 4\n", "output": "4\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "1\n1\n", "output": "1\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "1\n1000000000\n", "output": "1\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "2\n1 1\n", "output": "1\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "2\n1049 1098\n", "output": "1\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "2\n100 100\n", "output": "1\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "5\n1 2 3 2 1\n", "output": "3\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "15\n2 2 1 1 2 2 2 2 2 2 2 2 2 1 2\n", "output": "2\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "28\n415546599 415546599 415546599 415546599 415546599 415546599 415546599 415546599 415546599 2 802811737 802811737 802811737 802811737 802811737 802811737 802811737 802811737 1 550595901 550595901 550595901 550595901 550595901 550595901 550595901 550595901 550595901\n", "output": "6\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "45\n3 12 13 11 13 13 10 11 14 15 15 13 14 12 13 11 14 10 10 14 14 11 10 12 11 11 13 14 10 11 14 13 14 11 11 11 12 15 1 10 15 12 14 14 14\n", "output": "13\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "84\n1 3 4 5 6 5 6 7 8 9 7 4 5 4 2 5 1 1 1 3 2 7 7 8 10 9 5 6 5 2 3 3 3 3 3 2 4 8 6 5 8 9 8 7 9 3 4 4 4 2 2 1 6 4 9 5 9 9 10 7 10 4 5 4 2 4 3 3 4 4 6 6 6 9 10 12 7 5 9 8 5 3 3 2\n", "output": "8\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "170\n1 2 1 2 1 1 1 1 2 3 2 1 1 2 2 1 2 1 2 1 1 2 3 3 2 1 1 1 1 1 1 1 1 2 1 2 3 3 2 1 2 2 1 2 3 2 1 1 2 3 2 1 2 1 1 1 2 3 3 2 1 2 1 2 1 1 1 2 1 2 1 1 2 2 1 1 2 1 2 2 1 2 1 2 2 1 2 1 2 3 2 1 1 2 3 4 4 3 2 1 2 1 2 1 2 3 3 2 1 2 1 1 1 1 1 1 1 2 2 1 1 2 1 1 1 1 2 1 1 2 3 2 1 2 2 1 2 1 1 1 2 2 1 2 1 2 3 2 1 2 1 1 1 2 3 4 5 4 3 2 1 1 2 1 2 3 4 3 2 1\n", "output": "5\n", "metadata": {"func_name": null}}, {"type": "stdin_stdout", "input": "1\n5\n", "output": "1\n", "metadata": {"func_name": null}}]	livecodebench	deepcoder_13	13

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